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A179206 Smallest index k such that prime(k)*2^n * (prime(k)*2^n + 1) - 1 is prime. 1
1, 1, 1, 2, 1, 4, 3, 8, 1, 5, 5, 6, 6, 5, 1, 10, 16, 3, 13, 13, 37, 7, 1, 11, 1, 8, 18, 17, 6, 5, 15, 24, 12, 1, 16, 24, 7, 3, 9, 6, 17, 3, 15, 54, 24, 5, 16, 14, 8, 32, 1, 23, 17, 1, 62, 16, 23, 94, 65, 53, 70, 20, 9, 10, 9, 50, 12, 8, 12, 19, 155, 6, 46, 12, 2, 2, 12, 72, 20, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Define partial sums S(N) = Sum_{n=1..N} n and T(N) = Sum_{n=1..N} a(n). Then lim_{N->infinity} T(N)/S(N) -> approx 0.435.

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..8000

EXAMPLE

n=1: 2*2*(2*2 + 1) - 1 = 19 prime so k=1 as 2=prime(1).

n=2: 2*2^2*(2*2^2 + 1) - 1 = 71 prime so k=1 as 2=prime(1).

MAPLE

A179206 := proc(n) local k, pk; for k from 1 do pk := ithprime(k)*2^n ; if isprime(pk*(pk+1)-1) then return k; end if; end do: end proc:

seq(A179206(n), n=1..80) ; # R. J. Mathar, Jul 05 2010

CROSSREFS

Cf. A179205.

Sequence in context: A085930 A258863 A087207 * A331740 A074987 A294096

Adjacent sequences:  A179203 A179204 A179205 * A179207 A179208 A179209

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jul 02 2010

EXTENSIONS

More terms from R. J. Mathar, Jul 05 2010

STATUS

approved

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Last modified October 25 17:22 EDT 2021. Contains 348255 sequences. (Running on oeis4.)