

A152414


Least k(n) such that k(n)*2^n*(2^n1)1 or k(n)*2^n*(2^n1)+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
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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 1/2log(2)/4.
(End)


LINKS

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


EXAMPLE

1*2^1*(2^11)+1=3 is prime so k(1)=1.
1*2^2*(2^21)1=11 is prime, as well as 13, so k(2)=1.
2*2^3*(2^31)+1=113 is prime so k(3)=2.


PROG

(PARI) a(n) = {k = 1; while (! (isprime(k*2^n*(2^n1)+1)  isprime(k*2^n*(2^n1)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



