A118600 Palindromes in base 9 (written in base 9).

0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 22, 33, 44, 55, 66, 77, 88, 101, 111, 121, 131, 141, 151, 161, 171, 181, 202, 212, 222, 232, 242, 252, 262, 272, 282, 303, 313, 323, 333, 343, 353, 363, 373, 383, 404, 414, 424, 434, 444, 454, 464, 474, 484, 505, 515, 525, 535, 545

Offset: 1

Author

Martin Renner, May 08 2006

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1457

Crossrefs

Cf. A029955, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

Mathematica

(* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 62], Max@IntegerDigits@# < 9 &] (* Robert G. Wilson v, May 09 2006 *)

Python

from gmpy2 import digits
def palgenbase(l,b): # generator of palindromes in base b <=10 of length <= 2*l, written in base b
    if l > 0:
        yield 0
        for x in range(1,l+1):
            for y in range(b**(x-1),b**x):
                s = digits(y,b)
                yield int(s+s[-2::-1])
            for y in range(b**(x-1),b**x):
                s = digits(y,b)
                yield int(s+s[::-1])
A118600_list = list(palgenbase(3,9)) # Chai Wah Wu, Dec 01 2014

Python

from sympy import integer_log
from gmpy2 import digits
def A118600(n):
    if n == 1: return 0
    y = 9*(x:=9**integer_log(n>>1,9)[0])
    return int((s:=digits(n-x,9))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

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