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

1,1

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

Formula

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

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

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

Crossrefs

Cf. A101036, A126715, A187468.

Sequence in context: A359541 A377516 A069733 * A081755 A366538 A366536

Adjacent sequences: A187464 A187465 A187466 * A187468 A187469 A187470

Keyword

nonn

Author

Pierre CAMI, Mar 10 2011

Status

approved