A118597 Palindromes in base 6 (written in base 6).

0, 1, 2, 3, 4, 5, 11, 22, 33, 44, 55, 101, 111, 121, 131, 141, 151, 202, 212, 222, 232, 242, 252, 303, 313, 323, 333, 343, 353, 404, 414, 424, 434, 444, 454, 505, 515, 525, 535, 545, 555, 1001, 1111, 1221, 1331, 1441, 1551, 2002, 2112, 2222, 2332, 2442, 2552

Offset: 1

Author

Martin Renner, May 08 2006

Keywords

• nonn
• base

Comments

Also palindromes with no digit greater than 5. - Harvey P. Dale, Nov 26 2019

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A029953, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

Mathematica

(* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 125], Max@IntegerDigits@# < 6 &] (* Robert G. Wilson v, May 09 2006 *)
Select[FromDigits/@Tuples[Range[0,5],4],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 26 2019 *)

Python

from sympy import integer_log
from gmpy2 import digits
def A118597(n):
    if n == 1: return 0
    y = 6*(x:=6**integer_log(n>>1,6)[0])
    return int((s:=digits(n-x,6))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

Corrected and extended by Robert G. Wilson v, May 09 2006