A200654 Smallest k>0 such that k*p*(k*p+1)-1 and k*p*(k*p+1)+1 are twin primes, where p = n-th prime.

1, 1, 1, 3, 6, 27, 9, 2, 6, 7, 5, 14, 1, 5, 3, 10, 1, 15, 93, 36, 33, 5, 18, 1, 18, 1, 2, 28, 2, 10, 8, 1, 34, 11, 12, 3, 2, 116, 4, 52, 31, 29, 18, 42, 13, 32, 24, 71, 93, 122, 61, 75, 11, 141, 73, 31, 57, 36, 23, 43, 18, 15, 69, 33, 15, 10, 39, 8, 108, 29, 72, 7, 8, 62

Offset

1,4

Comments

(Sum_{n=1..N} k) / (Sum_{n=1..N} log(p)^2) tends to 1 as N increases.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

1*2*(1*2 + 1) - 1 = 5 and 1*2*(1*2 + 1) + 1 = 7;
5 and 7 are twin primes, so a(1)=1 as p(1)=2.
1*3*(1*3 + 1) - 1 = 11 and 1*3*(1*3 + 1) + 1 = 13;
11 and 13 are twin primes, so a(2)=1 as p(2)=3.

Maple

A200654 := proc(n)
    p := ithprime(n) ;
    for k from 1 do
        if isprime(k*p*(k*p+1)-1) and isprime(k*p*(k*p+1)+1) then
            return k;
        end if;
    end do:
    return 0 ;
end proc:
seq(A200654(n), n=1..80) ; # R. J. Mathar, Nov 26 2011

Crossrefs

Cf. A200778.

Sequence in context: A033194 A304051 A128437 * A208665 A256762 A064283

Adjacent sequences: A200651 A200652 A200653 * A200655 A200656 A200657

Keyword

nonn

Author

Pierre CAMI, Nov 20 2011

Status

approved