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.

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

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