%I #23 Jun 15 2024 01:02:29
%S 0,1,2,3,11,22,33,101,111,121,131,202,212,222,232,303,313,323,333,
%T 1001,1111,1221,1331,2002,2112,2222,2332,3003,3113,3223,3333,10001,
%U 10101,10201,10301,11011,11111,11211,11311,12021,12121,12221,12321,13031
%N Palindromes in base 4 (written in base 4).
%C 2*a(n) and 3*a(n) give palindromes in base 10 for any n. - _Arkadiusz Wesolowski_, Jun 22 2012
%C Equivalently, palindromes k (written in base 10) such that 3*k is a palindrome. - _Bruno Berselli_, Sep 12 2018
%t (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 290], Max@IntegerDigits@# < 4 &] (* _Robert G. Wilson v_, May 09 2006 *)
%o (Python)
%o from gmpy2 import digits
%o def A118595(n):
%o if n == 1: return 0
%o y = (x:=1<<(n.bit_length()-2&-2))<<2
%o 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
%Y Cf. A014192, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.
%K nonn,base
%O 1,3
%A _Martin Renner_, May 08 2006
%E More terms from _Robert G. Wilson v_, May 09 2006