A255309 - OEIS

%I #24 Jun 13 2022 10:55:20

%S 0,0,1,0,2,0,0,0,1,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N Number of times log_2 can be applied to n until the result is either 1 or not a power of 2. Here log_2 means the base-2 logarithm.

%H Antti Karttunen, <a href="/A255309/b255309.txt">Table of n, a(n) for n = 0..65537</a>

%F a(n) = 1 + a(log_2(n)) if n is a power of 2 except 1, 0 otherwise.

%o (PARI) nbi(n) = {my(nb = 0); if ((ispower(n, ,&m) && (m==2)) || (n==2), return(nbi(valuation(n, 2))+1);); nb;}

%o a(n) = { my(nb = 0); if ((ispower(n, ,&m) && (m==2)) || (n==2), return(nbi(valuation(n, 2))+1);); nb;} \\ _Michel Marcus_, Mar 11 2015; corrected Jun 13 2022

%o (PARI) A255309(n) = { my(k=0); while((n>1)&&!bitand(n,n-1),n = valuation(n,2); k++); (k); }; \\ _Antti Karttunen_, Sep 30 2018

%Y Cf. A000079 (2^n), A007814 (2-adic valuation of n), A209229, A255308.

%K nonn,easy

%O 0,5

%A _Paul Boddington_, Feb 20 2015

%E Extended up to a(128) by _Antti Karttunen_, Sep 30 2018