A046233 - OEIS

A046233

Numbers whose cube is palindromic in base 5.

0, 1, 6, 26, 126, 626, 3126, 15626, 78126, 390626, 1953126, 9765626, 48828126, 244140626, 1220703126, 6103515626, 30517578126, 152587890626, 762939453126, 3814697265626, 19073486328126, 95367431640626, 476837158203126

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OFFSET

1,3

COMMENTS

Note that '626' is itself palindromic.

Contains all A034474(n), n>=1, as a subset because (5^n+1)^3=5^(3n)+3*5^(2n)+3*5^n+1 is a symmetric string 100..00300..00300..001 in base 5. [R. J. Mathar, Jul 31 2008]

LINKS

Table of n, a(n) for n=1..23.

Patrick De Geest, World!Of Numbers, Palindromic cubes in bases 2 to 17.

PROG

(PARI) isok(k) = my(d=digits(k^3, 5)); Vecrev(d) == d; \\ Michel Marcus, Aug 02 2022

(Python)

from itertools import count, islice

from sympy.ntheory import is_palindromic as ispal

def agen(start=0): yield from (k for k in count(start) if ispal(k**3, 5))

print(list(islice(agen(), 10))) # Michael S. Branicky, Aug 02 2022

CROSSREFS

Cf. A034474, A046234.