A118595 Palindromes in base 4 (written in base 4).

0, 1, 2, 3, 11, 22, 33, 101, 111, 121, 131, 202, 212, 222, 232, 303, 313, 323, 333, 1001, 1111, 1221, 1331, 2002, 2112, 2222, 2332, 3003, 3113, 3223, 3333, 10001, 10101, 10201, 10301, 11011, 11111, 11211, 11311, 12021, 12121, 12221, 12321, 13031

Offset: 1

Author

Martin Renner, May 08 2006

Keywords

• nonn
• base

Comments

2*a(n) and 3*a(n) give palindromes in base 10 for any n. - Arkadiusz Wesolowski, Jun 22 2012

Equivalently, palindromes k (written in base 10) such that 3*k is a palindrome. - Bruno Berselli, Sep 12 2018

Crossrefs

Cf. A014192, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

Mathematica

(* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 290], Max@IntegerDigits@# < 4 &] (* Robert G. Wilson v, May 09 2006 *)

Python

from gmpy2 import digits
def A118595(n):
    if n == 1: return 0
    y = (x:=1<<(n.bit_length()-2&-2))<<2
    return int((s:=digits(n-x,4))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

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