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Palindromes in base 6 (written in base 6).
10

%I #18 Jun 15 2024 09:25:57

%S 0,1,2,3,4,5,11,22,33,44,55,101,111,121,131,141,151,202,212,222,232,

%T 242,252,303,313,323,333,343,353,404,414,424,434,444,454,505,515,525,

%U 535,545,555,1001,1111,1221,1331,1441,1551,2002,2112,2222,2332,2442,2552

%N Palindromes in base 6 (written in base 6).

%C Also palindromes with no digit greater than 5. - _Harvey P. Dale_, Nov 26 2019

%H Harvey P. Dale, <a href="/A118597/b118597.txt">Table of n, a(n) for n = 1..1000</a>

%t (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 125], Max@IntegerDigits@# < 6 &] (* _Robert G. Wilson v_, May 09 2006 *)

%t Select[FromDigits/@Tuples[Range[0,5],4],PalindromeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 26 2019 *)

%o (Python)

%o from sympy import integer_log

%o from gmpy2 import digits

%o def A118597(n):

%o if n == 1: return 0

%o y = 6*(x:=6**integer_log(n>>1,6)[0])

%o return int((s:=digits(n-x,6))+s[-2::-1] if n<x+y else (s:=digits(n-y,6))+s[::-1]) # _Chai Wah Wu_, Jun 14 2024

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

%K nonn,base

%O 1,3

%A _Martin Renner_, May 08 2006

%E Corrected and extended by _Robert G. Wilson v_, May 09 2006