A074981 -id:A074981 - cp's OEIS frontend

A110222 Palindromic numbers which are not the absolute difference of a cube and a square.

6, 66, 77, 88, 111, 181, 202, 363, 383, 434, 454, 474, 494, 555, 565, 595, 606, 646, 666, 707, 717, 747, 787, 818, 838, 858, 929, 949, 959, 979, 989, 1221, 1551, 1661, 2002, 2442, 2662, 3003, 3443, 3773, 3883, 4114, 4334, 4444, 4774, 4884, 5005, 5115, 5335

Offset: 1

Robert G. Wilson v, Jul 16 2005

The palindromes in A110223.

Cf. A109879, A074981, A110223.

NextPalindrome[n_] := Block[ {l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[ idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[ idn, Ceiling[l/2]]]] > FromDigits[ Take[ idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[ idn, Ceiling[l/2]], Reverse[ Take[ idn, Floor[l/2]]]]], idfhn = FromDigits[ Take[ idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[ idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]]]]]]]]; t1 = NestList[ NextPalindrome, 0, 130]; t2 = Union[ Flatten[ Table[ Select[ Table[ Abs[n^3 - m^2], {m, 0, 10000}], # < 10^3 &], {n, -5000, 5000}]]]; Take[ Complement[t1, Intersection[t1, t2]], 50]

A253237 Conjectured largest perfect power k such that k+n is also a perfect power, or 0 if no such k exists.

Original entry on oeis.org

8, 25, 125, 121, 27, 0, 32761, 97336, 64000, 2187, 3364, 2197, 4900, 0, 1295029, 128, 143384152904, 343, 503284356, 196, 100, 2187, 2025, 542939080312, 144, 6436343, 216, 131044, 196, 6859, 225, 7744, 256, 0, 1296, 1728, 14348907, 1331, 10609, 2704, 400, 0, 441, 125, 9216

Offset: 1

Eric Chen, Apr 04 2015

Only a(1) is proven, all other terms (even including a(2)) are only conjectured.
These terms are searched up to 10^18, and no terms are greater than 10^12.
a(n) = A103953(n) for n in A076438.
See A076427 for further information. - M. F. Hasler, Apr 09 2015

Eric Weisstein's World of Mathematics, Pillai's Conjecture.
Wikipedia, Catalan's conjecture.
Wikipedia, Hall's conjecture.

Cf. A001597, A074981, A076427, A076438, A103953.

a(A074981(n)) = 0.

cp's OEIS Frontend

A110222 Palindromic numbers which are not the absolute difference of a cube and a square.

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