A118596 Palindromes in base 5 (written in base 5).

0, 1, 2, 3, 4, 11, 22, 33, 44, 101, 111, 121, 131, 141, 202, 212, 222, 232, 242, 303, 313, 323, 333, 343, 404, 414, 424, 434, 444, 1001, 1111, 1221, 1331, 1441, 2002, 2112, 2222, 2332, 2442, 3003, 3113, 3223, 3333, 3443, 4004, 4114, 4224, 4334, 4444, 10001

Offset: 1

Author

Martin Renner, May 08 2006

Keywords

• nonn
• base

Comments

Equivalently, palindromes k (written in base 10) such that 2*k is a palindrome. - Bruno Berselli, Sep 12 2018

Crossrefs

Cf. A029952, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

Mathematica

(* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 198], Max@IntegerDigits@# < 5 &] (* Robert G. Wilson v, May 09 2006 *)
Select[FromDigits/@IntegerDigits[Range[1000],5],PalindromeQ] (* Fred Patrick Doty, Aug 12 2017 *)

PARI

is(n)=if(n<5, return(n>=0)); my(d=digits(n)); vecmax(d)<5 && Vecrev(d)==d \\ Charles R Greathouse IV, Aug 22 2017

Python

from sympy import integer_log
from gmpy2 import digits
def A118596(n):
    if n == 1: return 0
    y = 5*(x:=5**integer_log(n>>1,5)[0])
    return int((s:=digits(n-x,5))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

More terms from Robert G. Wilson v, May 09 2006