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A152414 Least k(n) such that k(n)*2^n*(2^n-1)-1 or k(n)*2^n*(2^n-1)+1 is prime or both primes. 8
1, 1, 2, 1, 1, 3, 3, 6, 1, 1, 4, 2, 5, 3, 9, 8, 4, 1, 3, 4, 36, 5, 2, 4, 10, 4, 18, 3, 21, 9, 6, 1, 6, 8, 12, 2, 51, 1, 2, 2, 21, 6, 6, 12, 1, 5, 5, 3, 10, 1, 11, 53, 9, 4, 3, 2, 1, 5, 12, 10, 9, 8, 5, 9, 7, 6, 62, 29, 16, 51, 12, 3, 30, 56, 2, 23, 70, 3, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

As n increases, sum k(n) for i=1 to n / sum n for i=1 to n tends to 1/4. All values in b152414 verified and primes certified using PFGW from Primeform group.

Contribution from Pierre CAMI, Dec 04 2008: (Start)

for n even sum k(2*n) for i=1 to n / sum 2*n for i=1 to n tends to log(2)/4.

for n odd sum k(2*n+1) for i=0 to n / sum 2*n+1 for i=1 to n tends to 1/2-log(2)/4.

(End)

LINKS

Pierre CAMI, Table of n, a(n) for n=1..4000

EXAMPLE

1*2^1*(2^1-1)+1=3 is prime so k(1)=1.

1*2^2*(2^2-1)-1=11 is prime, as well as 13, so k(2)=1.

2*2^3*(2^3-1)+1=113 is prime so k(3)=2.

PROG

(PARI) a(n) = {k = 1; while (! (isprime(k*2^n*(2^n-1)+1) || isprime(k*2^n*(2^n-1)-1)), k++); return (k); } \\ Michel Marcus, Mar 07 2013

CROSSREFS

Sequence in context: A035636 A104554 A293304 * A184834 A276777 A219876

Adjacent sequences:  A152411 A152412 A152413 * A152415 A152416 A152417

KEYWORD

nonn

AUTHOR

Pierre CAMI, Dec 03 2008

STATUS

approved

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Last modified August 21 05:32 EDT 2019. Contains 326162 sequences. (Running on oeis4.)