1,3

The number of n-digit terms is given by A225367. - M. F. Hasler, May 05 2013 [Moved here on May 08 2013]

Digit-wise application of A000578 (and also superposition of a(n) with its horizontal OR vertical reflection) yields A006072. - M. F. Hasler, May 08 2013

Equivalently, palindromes k (written in base 10) such that 4*k is a palindrome. - Bruno Berselli, Sep 12 2018

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Palindromic Number

Eric Weisstein's World of Mathematics, Ternary

(* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 1110], Max@IntegerDigits@# < 3 &] (* Robert G. Wilson v, May 09 2006 *)

Select[FromDigits/@Tuples[{0, 1, 2}, 8], IntegerDigits[#]==Reverse[ IntegerDigits[ #]]&] (* Harvey P. Dale, Apr 20 2015 *)

(PARI) {for(l=1, 5, u=vector((l+1)\2, i, 10^(i-1)+(2*i-1<l)*10^(l-i))~; forvec(v=vector((l+1)\2, i, [l>1&&i==1, 2]), print1(v*u", ")))} \\ The n-th term could be produced by using (partial sums of) A225367 to skip all shorter terms, and then skipping the adequate number of vectors v until n is reached. - M. F. Hasler, May 08 2013

(SageMath)

[int(n.str(base=3)) for n in (0..757) if Word(n.digits(3)).is_palindrome()] # Peter Luschny, Sep 13 2018

(Python)

from itertools import count, islice, product

def agen(): # generator of terms

yield from [0, 1, 2]

for d in count(2):

for start in "12":

for rest in product("012", repeat=d//2-1):

left = start + "".join(rest)

for mid in [[""], ["0", "1", "2"]][d%2]:

yield int(left + mid + left[::-1])

print(list(islice(agen(), 42))) # Michael S. Branicky, Mar 29 2022

(Python)

from sympy import integer_log

from gmpy2 import digits

def A118594(n):

if n == 1: return 0

y = 3*(x:=3**integer_log(n>>1, 3)[0])

return int((s:=digits(n-x, 3))+s[-2::-1] if n<x+y else (s:=digits(n-y, 3))+s[::-1]) # Chai Wah Wu, Jun 14 2024

Cf. A007089, A014190, A057148, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Sequence in context: A018711 A018737 A162468 * A263720 A235609 A376688

Adjacent sequences: A118591 A118592 A118593 * A118595 A118596 A118597

nonn,base,easy

Martin Renner, May 08 2006

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

a(40) and beyond from Michael S. Branicky, Mar 29 2022

approved