A282459 - OEIS

%I #23 Feb 16 2017 03:19:42

%S 0,0,0,0,0,1,1,0,2,1,0,2,2,1,3,2,1,2,3,1,4,3,0,3,2,2,4,2,3,4,2,1,4,4,

%T 1,4,4,0,3,4,3,3,4,2,5,3,3,4,5,3,4,4,0,4,4,1,4,3,2,5,4,4,4,6,3,4,4,2,

%U 6,3,3,4,4,3,7,5,3,5,5,3,5,6,2,4,4,2,5,4,5,6,3,3,6,5,3,6,6,1,5,3,2,5,5,4,6,5,3,4,6

%N Number of composite numbers of the form 2*n - 2^k + 1 (k > 0, 2^k < 2*n + 1).

%C It is conjectured that a(n) > 0 for all n > 52. See related conjecture and findings in A039669. Also see the graph of this sequence.

%H Altug Alkan, <a href="/A282459/b282459.txt">Table of n, a(n) for n = 0..10000</a>

%e a(7) = 0 because 2*7 + 1 - 2^1 = 13, 2*7 + 1 - 2^2 = 11, 2*7 + 1 - 2^3 = 7 are prime numbers.

%o (PARI) isA002808(n) = n>1 && !isprime(n);

%o a(n) = sum(k=1, log(2*n+1)\log(2), isA002808(2*n+1-2^k))

%Y Cf. A002808, A039669, A067526, A109925.

%K nonn

%O 0,9

%A _Altug Alkan_, Feb 15 2017