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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 T(N)/S(N) -> approx 0.435 as N->infinity. 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: A058354 A085930 A087207 * A074987 A128280 A182177 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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