A085804 Least k such that n^n + k is a palindrome.

0, 0, 6, 6, 98, 8, 885, 545, 4294, 1, 542971, 567942, 4985950, 34463095, 817539359, 3335212865, 1825278551, 60542888969, 351980024812, 6758401, 13316726728064, 355067132000559, 10940544943498235, 100371505302529555, 98630474467606263

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..702

Mathematica

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]]]]]]]]; f[n_] := Block[{}, If[ FromDigits[ Reverse[ IntegerDigits[n^n]]] == n^n, 0, NextPalindrome[n^n] - n^n]];
nLP[cn_Integer]:=Module[{s, len, half, left, pal, fdpal}, s=IntegerDigits[cn]; len=Length[s]; half=Ceiling[len/2]; left=Take[s, half]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; fdpal=FromDigits[pal]; Which[cn==9, 11, fdpal>cn, fdpal, True, left=IntegerDigits[ FromDigits[left]+1]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; FromDigits[pal]]]; Join[{0, 0}, Table[With[{c=n^n}, nLP[c]-c], {n, 3, 30}]] (* Harvey P. Dale, Aug 28 2025 *)

Crossrefs

Sequence in context: A347916 A361738 A320824 * A012125 A267139 A170915

Adjacent sequences: A085801 A085802 A085803 * A085805 A085806 A085807

Keyword

base,nonn

Author

Jason Earls, Jul 24 2003

Extensions

Edited and extended by Robert G. Wilson v, Jul 26 2003

Status

approved