## S000939

In base 8, these positive numbers and their squares are palindromic.

1, 2, 3, 6, 9, 27, 65, 73, 81, 195, 219, 513, 585, 1539, 1755, 4097, 4161, 4225, 4617, 4681, 12291, 12483, 12675, 13851, 32769, 33345, 36873, 37449, 98307, 100035, 110619, 262145, 262657, 263169, 266305, 266817, 294921, 295433, 299081, 299593, 786435, 787971

1

Written in base 8, the numbers are 1, 2, 3, 6, 11, 33, 101, 111, 121, 303, 333, 1001, 1111, 3003, 3333, 10001,. The squares are 1, 4, 11, 44, 121, 1331, 10201, 12321, 14641, 112211, 135531, 1002001, 1234321, 11022011, 13577531, 100020001,.

T. D. Noe, Plot of 360 terms

T. D. Noe, Table of 360 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 = 8; 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