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

1,3

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

Links

Table of n, a(n) for n=1..44.

Mathematica

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

Prog

(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 n<x+y else (s:=digits(n-y, 4))+s[::-1]) # Chai Wah Wu, Jun 14 2024

Crossrefs

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

Sequence in context: A215952 A276375 A128921 * A229549 A229804 A241096

Adjacent sequences: A118592 A118593 A118594 * A118596 A118597 A118598

Keyword

nonn,base

Author

Martin Renner, May 08 2006

Extensions

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

Status

approved