## S000936

In base 5, these positive numbers and their squares are palindromic.

1, 2, 6, 26, 31, 126, 156, 626, 651, 756, 3126, 3276, 3756, 15626, 15751, 16276, 18756, 78126, 78876, 81276, 93756, 390626, 391251, 393876, 406276, 468756, 1953126, 1956876, 1968876, 2031276, 2343756, 9765626, 9768751, 9781876, 9843876, 10156276, 11718756

1

Written in base 5, the numbers are 1, 2, 11, 101, 111, 1001, 1111, 10001, 10101, 11011, 100001, 101101,… whose squares are 1, 4, 121, 10201, 12321, 1002001, 1234321, 100020001, 102030201, 121242121, 10000200001, 10221412201,.

T. D. Noe, Plot of 111 terms

T. D. Noe, Table of 111 terms

Eric W. Weisstein, MathWorld: Palindromic Number

(Mma) makePalindrome[n_Integer, b_Integer, del_] := Module[{c = IntegerDigits[n, b], d}, d = If[del, Join[c, Reverse[Most[c]]], Join[c, Reverse[c]]]; FromDigits[d]]; palindromeQ[n_, b_] := Module[{d = IntegerDigits[n, b]}, d == Reverse[d]]; b = 5; t = {}; Do[Do[Do[d = makePalindrome[i, b, j]; e = FromDigits[IntegerDigits[d], b]; If[palindromeQ[e^2, b], AppendTo[t, e]], {i, b^(n - 1), b^n - 1}], {j, {True, False}}], {n, Floor[0.5 + 10*Log[3]/Log[b]]}]

Cf. S000934-S000941.

nonn,base

T. D. Noe, Aug 26 2016