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

%I #17 Jan 29 2019 23:59:20

%S 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,

%T 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,

%U 22,23,130,7,22,16,18,2

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

%C 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.

%C 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

%H Pierre CAMI, <a href="/A187467/b187467.txt">Table of n, a(n) for n = 1..4100</a>

%F a(n) = primepi(A126715(n)). - _T. D. Noe_, Mar 10 2011

%F a(n) >= A179289(n). - _R. J. Mathar_, Mar 19 2011

%p 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

%Y Cf. A101036, A126715, A187468.

%K nonn

%O 1,1

%A _Pierre CAMI_, Mar 10 2011

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