A282459 Number of composite numbers of the form 2*n - 2^k + 1 (k > 0, 2^k < 2*n + 1).

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, 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, 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

Offset: 0

Author

Altug Alkan, Feb 15 2017

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Altug Alkan, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002808, A039669, A067526, A109925.

Programs

PARI

isA002808(n) = n>1 && !isprime(n);
a(n) = sum(k=1, log(2*n+1)\log(2), isA002808(2*n+1-2^k))