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%I #26 Jul 10 2022 03:57:11
%S 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 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 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 Exponent of highest power of 8 dividing n.
%C 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 Kurt Mahler, p-adic numbers and their functions, 2nd ed., Cambridge University press, 1981.
%H Antti Karttunen, <a href="/A244413/b244413.txt">Table of n, a(n) for n = 1..65536</a>
%F n = 8^a(n)*m with a(n) nonnegative integer such that 8 does not divide m, for n >= 1.
%F O.g.f.: Sum_{k>=1} x^(8^k)/(1-x^(8^k)).
%F Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/7. - _Amiram Eldar_, Jan 17 2022
%t Table[IntegerExponent[n, 8], {n, 1, 100}] (* _Amiram Eldar_, Sep 14 2020 *)
%o (PARI) A244413(n) = valuation(n,8); \\ _Antti Karttunen_, Oct 07 2017
%o (Python)
%o def A244413(n): return (~n&n-1).bit_length()//3 # _Chai Wah Wu_, Jul 09 2022
%Y Cf. A007814, A007949, A235127, A112765, A122841, A214411.
%K nonn,easy
%O 1,64
%A _Wolfdieter Lang_, Jun 27 2014
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