This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A244413 #34 Jul 26 2024 05:26:05
%S A244413 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,
%T A244413 0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,
%U A244413 0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0
%N A244413 Exponent of highest power of 8 dividing n.
%C A244413 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).
%D A244413 Kurt Mahler, p-adic numbers and their functions, 2nd ed., Cambridge University press, 1981.
%H A244413 Antti Karttunen, <a href="/A244413/b244413.txt">Table of n, a(n) for n = 1..65536</a>
%F A244413 n = 8^a(n)*m with a(n) nonnegative integer such that 8 does not divide m, for n >= 1.
%F A244413 O.g.f.: Sum_{k>=1} x^(8^k)/(1-x^(8^k)).
%F A244413 Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/7. - _Amiram Eldar_, Jan 17 2022
%F A244413 a(n) = floor(A007814(n)/3). - _Alan Michael Gómez Calderón_, Jul 25 2024
%t A244413 Table[IntegerExponent[n, 8], {n, 1, 100}] (* _Amiram Eldar_, Sep 14 2020 *)
%o A244413 (PARI) A244413(n) = valuation(n,8); \\ _Antti Karttunen_, Oct 07 2017
%o A244413 (Python)
%o A244413 def A244413(n): return (~n&n-1).bit_length()//3 # _Chai Wah Wu_, Jul 09 2022
%Y A244413 Cf. A007814, A007949, A235127, A112765, A122841, A214411.
%K A244413 nonn,easy
%O A244413 1,64
%A A244413 _Wolfdieter Lang_, Jun 27 2014