A187467 Least k > 1 such that prime(k)*2^n - 1 is prime, or zero if never prime.

2, 2, 2, 2, 4, 2, 2, 3, 4, 3, 2, 3, 11, 3, 22, 7, 4, 2, 18, 7, 4, 23, 6, 23, 18, 5, 44, 23, 4, 98, 14, 3, 11, 2, 11, 7, 11, 2, 18, 28, 8, 16, 2, 102, 4, 9, 11, 3, 8, 5, 174, 24, 63, 3, 2, 103, 22, 23, 130, 7, 22, 16, 18, 2

Offset: 1

Author

Pierre CAMI, Mar 10 2011

Keywords

• nonn

Comments

As N increases, it appears that (Sum_{i=1..N} a(i)) / (Sum_{i=1..N} i) tends to 1/2, i.e., the partial sums grow roughly proportional to the triangular numbers.

It is conjectured that a(42228) is the first 0 term. This corresponds to the first Riesel number, 509203, which happens to be prime. See A101036. - T. D. Noe, Mar 23 2011

Links

• Pierre CAMI, Table of n, a(n) for n = 1..4100

Crossrefs

Cf. A101036, A126715, A187468.

Programs

Maple

A187467 := proc(n) local k; for k from 2 do if isprime( ithprime(k)*2^n-1) then return k; end if; end do: end proc: # R. J. Mathar, Mar 19 2011

Formula

a(n) = primepi(A126715(n)). - T. D. Noe, Mar 10 2011

a(n) >= A179289(n). - R. J. Mathar, Mar 19 2011