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Even number not the sum of two base $2$ palindromes
2
$begingroup$
What's the least positive even number not a sum of two base $2$ palindromes? I've checked and it must be over $100$ since all up to $100$ are such sums. [Or, which to me seems unlikely, are all even numbers such sums?]
Base $2$ palindromes entry o.e.i.s. http://oeis.org/A006995
palindrome
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
$endgroup$
add a comment |
2
$begingroup$
What's the least positive even number not a sum of two base $2$ palindromes? I've checked and it must be over $100$ since all up to $100$ are such sums. [Or, which to me seems unlikely, are all even numbers such sums?]
Base $2$ palindromes entry o.e.i.s. http://oeis.org/A006995
palindrome
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
$endgroup$
$begingroup$
leading $0$'s not allowed, I presume?
$endgroup$
– Anvit
Dec 27 '18 at 17:39
$begingroup$
@Anvit Yes, not with leading $0'$s -- all palindromes are thus odd numbers.
$endgroup$
– coffeemath
Dec 27 '18 at 17:49
add a comment |
2
2
2
1
$begingroup$
What's the least positive even number not a sum of two base $2$ palindromes? I've checked and it must be over $100$ since all up to $100$ are such sums. [Or, which to me seems unlikely, are all even numbers such sums?]
Base $2$ palindromes entry o.e.i.s. http://oeis.org/A006995
palindrome
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
$endgroup$
What's the least positive even number not a sum of two base $2$ palindromes? I've checked and it must be over $100$ since all up to $100$ are such sums. [Or, which to me seems unlikely, are all even numbers such sums?]
Base $2$ palindromes entry o.e.i.s. http://oeis.org/A006995
palindrome
palindrome
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
edited Jan 22 at 1:42
J. W. Tanner
2,9191217
2,9191217
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
asked Dec 27 '18 at 17:29
coffeemathcoffeemath
2,8571415
2,8571415
$begingroup$
leading $0$'s not allowed, I presume?
$endgroup$
– Anvit
Dec 27 '18 at 17:39
$begingroup$
@Anvit Yes, not with leading $0'$s -- all palindromes are thus odd numbers.
$endgroup$
– coffeemath
Dec 27 '18 at 17:49
add a comment |
$begingroup$
leading $0$'s not allowed, I presume?
$endgroup$
– Anvit
Dec 27 '18 at 17:39
$begingroup$
@Anvit Yes, not with leading $0'$s -- all palindromes are thus odd numbers.
$endgroup$
– coffeemath
Dec 27 '18 at 17:49
$begingroup$
leading $0$'s not allowed, I presume?
$endgroup$
– Anvit
Dec 27 '18 at 17:39
$begingroup$
leading $0$'s not allowed, I presume?
$endgroup$
– Anvit
Dec 27 '18 at 17:39
$begingroup$
@Anvit Yes, not with leading $0'$s -- all palindromes are thus odd numbers.
$endgroup$
– coffeemath
Dec 27 '18 at 17:49
$begingroup$
@Anvit Yes, not with leading $0'$s -- all palindromes are thus odd numbers.
$endgroup$
– coffeemath
Dec 27 '18 at 17:49
add a comment |
1 Answer
1
active
oldest
votes
1
$begingroup$
$176$ is your first culprit. Here's the Pseudocode (Python) I used. List was taken from OEIS.
from itertools import product
mylist = [0,1,3,5,7,9,15,17,21,27,31,33,45,51,63,65,73,85,
93,99,107,119,127,129,153,165,189,195,219,231,255,
257,273,297,313,325,341,365,381,387,403,427,443,
455,471,495,511,513,561,585,633,645,693,717,765,
771,819,843]
valids = set()
for i,j in product(mylist,mylist):
valids.add(i+j)
for i in range(0,850,2):
if i not in valids:
print(i)
break
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
$endgroup$
$begingroup$
Thanks! I don't have (or know how to program) much knowledge on python or other CAS which would allow me to check.
$endgroup$
– coffeemath
Dec 27 '18 at 17:51
1
$begingroup$
@coffeemath You can check 176 by hand aswell since you do have a list of binary palindromes :P
$endgroup$
– Anvit
Dec 27 '18 at 17:53
1
$begingroup$
@coffeemath or, in any computer language, you can download the first ten thousand palindromes to a text file from oeis.org/A006995/b006995.txt and then write a program to add them in pairs, finally sort them and report those even numbers not achieved up to some bound. In C++ I can make a set type, it will automatically keep the pairwise sums in sorted order and not keep duplicates
$endgroup$
– Will Jagy
Dec 27 '18 at 18:56
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
1
$begingroup$
$176$ is your first culprit. Here's the Pseudocode (Python) I used. List was taken from OEIS.
from itertools import product
mylist = [0,1,3,5,7,9,15,17,21,27,31,33,45,51,63,65,73,85,
93,99,107,119,127,129,153,165,189,195,219,231,255,
257,273,297,313,325,341,365,381,387,403,427,443,
455,471,495,511,513,561,585,633,645,693,717,765,
771,819,843]
valids = set()
for i,j in product(mylist,mylist):
valids.add(i+j)
for i in range(0,850,2):
if i not in valids:
print(i)
break
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
$endgroup$
$begingroup$
Thanks! I don't have (or know how to program) much knowledge on python or other CAS which would allow me to check.
$endgroup$
– coffeemath
Dec 27 '18 at 17:51
1
$begingroup$
@coffeemath You can check 176 by hand aswell since you do have a list of binary palindromes :P
$endgroup$
– Anvit
Dec 27 '18 at 17:53
1
$begingroup$
@coffeemath or, in any computer language, you can download the first ten thousand palindromes to a text file from oeis.org/A006995/b006995.txt and then write a program to add them in pairs, finally sort them and report those even numbers not achieved up to some bound. In C++ I can make a set type, it will automatically keep the pairwise sums in sorted order and not keep duplicates
$endgroup$
– Will Jagy
Dec 27 '18 at 18:56
add a comment |
1
$begingroup$
$176$ is your first culprit. Here's the Pseudocode (Python) I used. List was taken from OEIS.
from itertools import product
mylist = [0,1,3,5,7,9,15,17,21,27,31,33,45,51,63,65,73,85,
93,99,107,119,127,129,153,165,189,195,219,231,255,
257,273,297,313,325,341,365,381,387,403,427,443,
455,471,495,511,513,561,585,633,645,693,717,765,
771,819,843]
valids = set()
for i,j in product(mylist,mylist):
valids.add(i+j)
for i in range(0,850,2):
if i not in valids:
print(i)
break
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
$endgroup$
$begingroup$
Thanks! I don't have (or know how to program) much knowledge on python or other CAS which would allow me to check.
$endgroup$
– coffeemath
Dec 27 '18 at 17:51
1
$begingroup$
@coffeemath You can check 176 by hand aswell since you do have a list of binary palindromes :P
$endgroup$
– Anvit
Dec 27 '18 at 17:53
1
$begingroup$
@coffeemath or, in any computer language, you can download the first ten thousand palindromes to a text file from oeis.org/A006995/b006995.txt and then write a program to add them in pairs, finally sort them and report those even numbers not achieved up to some bound. In C++ I can make a set type, it will automatically keep the pairwise sums in sorted order and not keep duplicates
$endgroup$
– Will Jagy
Dec 27 '18 at 18:56
add a comment |
1
1
1
$begingroup$
$176$ is your first culprit. Here's the Pseudocode (Python) I used. List was taken from OEIS.
from itertools import product
mylist = [0,1,3,5,7,9,15,17,21,27,31,33,45,51,63,65,73,85,
93,99,107,119,127,129,153,165,189,195,219,231,255,
257,273,297,313,325,341,365,381,387,403,427,443,
455,471,495,511,513,561,585,633,645,693,717,765,
771,819,843]
valids = set()
for i,j in product(mylist,mylist):
valids.add(i+j)
for i in range(0,850,2):
if i not in valids:
print(i)
break
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
$endgroup$
$176$ is your first culprit. Here's the Pseudocode (Python) I used. List was taken from OEIS.
from itertools import product
mylist = [0,1,3,5,7,9,15,17,21,27,31,33,45,51,63,65,73,85,
93,99,107,119,127,129,153,165,189,195,219,231,255,
257,273,297,313,325,341,365,381,387,403,427,443,
455,471,495,511,513,561,585,633,645,693,717,765,
771,819,843]
valids = set()
for i,j in product(mylist,mylist):
valids.add(i+j)
for i in range(0,850,2):
if i not in valids:
print(i)
break
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
answered Dec 27 '18 at 17:45
AnvitAnvit
1,735419
1,735419
$begingroup$
Thanks! I don't have (or know how to program) much knowledge on python or other CAS which would allow me to check.
$endgroup$
– coffeemath
Dec 27 '18 at 17:51
1
$begingroup$
@coffeemath You can check 176 by hand aswell since you do have a list of binary palindromes :P
$endgroup$
– Anvit
Dec 27 '18 at 17:53
1
$begingroup$
@coffeemath or, in any computer language, you can download the first ten thousand palindromes to a text file from oeis.org/A006995/b006995.txt and then write a program to add them in pairs, finally sort them and report those even numbers not achieved up to some bound. In C++ I can make a set type, it will automatically keep the pairwise sums in sorted order and not keep duplicates
$endgroup$
– Will Jagy
Dec 27 '18 at 18:56
add a comment |
$begingroup$
Thanks! I don't have (or know how to program) much knowledge on python or other CAS which would allow me to check.
$endgroup$
– coffeemath
Dec 27 '18 at 17:51
1
$begingroup$
@coffeemath You can check 176 by hand aswell since you do have a list of binary palindromes :P
$endgroup$
– Anvit
Dec 27 '18 at 17:53
1
$begingroup$
@coffeemath or, in any computer language, you can download the first ten thousand palindromes to a text file from oeis.org/A006995/b006995.txt and then write a program to add them in pairs, finally sort them and report those even numbers not achieved up to some bound. In C++ I can make a set type, it will automatically keep the pairwise sums in sorted order and not keep duplicates
$endgroup$
– Will Jagy
Dec 27 '18 at 18:56
$begingroup$
Thanks! I don't have (or know how to program) much knowledge on python or other CAS which would allow me to check.
$endgroup$
– coffeemath
Dec 27 '18 at 17:51
$begingroup$
Thanks! I don't have (or know how to program) much knowledge on python or other CAS which would allow me to check.
$endgroup$
– coffeemath
Dec 27 '18 at 17:51
1
1
$begingroup$
@coffeemath You can check 176 by hand aswell since you do have a list of binary palindromes :P
$endgroup$
– Anvit
Dec 27 '18 at 17:53
$begingroup$
@coffeemath You can check 176 by hand aswell since you do have a list of binary palindromes :P
$endgroup$
– Anvit
Dec 27 '18 at 17:53
1
1
$begingroup$
@coffeemath or, in any computer language, you can download the first ten thousand palindromes to a text file from oeis.org/A006995/b006995.txt and then write a program to add them in pairs, finally sort them and report those even numbers not achieved up to some bound. In C++ I can make a set type, it will automatically keep the pairwise sums in sorted order and not keep duplicates
$endgroup$
– Will Jagy
Dec 27 '18 at 18:56
$begingroup$
@coffeemath or, in any computer language, you can download the first ten thousand palindromes to a text file from oeis.org/A006995/b006995.txt and then write a program to add them in pairs, finally sort them and report those even numbers not achieved up to some bound. In C++ I can make a set type, it will automatically keep the pairwise sums in sorted order and not keep duplicates
$endgroup$
– Will Jagy
Dec 27 '18 at 18:56
add a comment |
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$begingroup$
leading $0$'s not allowed, I presume?
$endgroup$
– Anvit
Dec 27 '18 at 17:39
$begingroup$
@Anvit Yes, not with leading $0'$s -- all palindromes are thus odd numbers.
$endgroup$
– coffeemath
Dec 27 '18 at 17:49