OFFSET
1,64
COMMENTS
This is the member g = 8 in the g-family of sequences, g integer >= 2, call it phi(g,n), n >= 1. In the Mahler reference, Lemma 2, pp. 6-7, this exponent is called f = -phi if g divides r = n (s = 1 there), and f = 0 if g does not divide r = n (s = 1 there).
REFERENCES
Kurt Mahler, p-adic numbers and their functions, 2nd ed., Cambridge University press, 1981.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65536
FORMULA
n = 8^a(n)*m with a(n) nonnegative integer such that 8 does not divide m, for n >= 1.
O.g.f.: Sum_{k>=1} x^(8^k)/(1-x^(8^k)).
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/7. - Amiram Eldar, Jan 17 2022
a(n) = floor(A007814(n)/3). - Alan Michael Gómez Calderón, Jul 25 2024
MATHEMATICA
Table[IntegerExponent[n, 8], {n, 1, 100}] (* Amiram Eldar, Sep 14 2020 *)
PROG
(PARI) A244413(n) = valuation(n, 8); \\ Antti Karttunen, Oct 07 2017
(Python)
def A244413(n): return (~n&n-1).bit_length()//3 # Chai Wah Wu, Jul 09 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 27 2014
STATUS
approved