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Index of 2^n within sequence of numbers of form 2^i*7^j.
1

%I #16 Jan 11 2018 09:10:53

%S 1,2,3,5,7,9,12,15,18,22,26,30,35,40,45,51,57,64,71,78,86,94,102,111,

%T 120,129,139,149,159,170,181,193,205,217,230,243,256,270,284,298,313,

%U 328,343,359,375,392,409,426,444,462,480,499,518,537,557,577,597,618,639,661,683

%N Index of 2^n within sequence of numbers of form 2^i*7^j.

%H Charles R Greathouse IV, <a href="/A025693/b025693.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ kn^2 + O(n) with k = log(7)/log(2) - log(7)^2/log(2)^2. - _Charles R Greathouse IV_, Jun 28 2011

%o (PARI) a(n)=my(N=7<<n);sum(k=0,log(N)\log(7)-1,#binary(N\=7)) \\ _Charles R Greathouse IV_, Jun 28 2011

%o (PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N<<=1, 7)); \\ _Charles R Greathouse IV_, Jan 11 2018

%o (PARI) first(n)=my(s, N=1/2); vector(n+1, i, s+=logint(N<<=1, 7)+1) \\ _Charles R Greathouse IV_, Jan 11 2018

%Y Cf. A003591.

%K nonn,easy

%O 0,2

%A _David W. Wilson_

%E An incorrect g.f. was deleted by _N. J. A. Sloane_, Sep 16 2009