A200778 Least k > 0 such that k*p*(k*p-1)-1 and k*p*(k*p-1)+1 is a twin prime pair, where p=prime(n).

2, 1, 5, 1, 2, 3, 3, 13, 9, 8, 10, 43, 69, 15, 17, 50, 3, 42, 1, 2, 3, 3, 20, 33, 3, 44, 7, 35, 49, 9, 6, 189, 15, 1, 113, 21, 7, 154, 3, 3, 18, 12, 29, 33, 20, 6, 27, 3, 2, 3, 23, 11, 10, 12, 18, 137, 41, 12, 36, 29, 54, 17, 10, 59, 55, 3, 51, 36

Offset

1,1

Comments

Limit_{N->oo} (Sum_{n=1..N} k(n)) / (Sum_{n=1..N} log(p(n))^2) = 1.

Links

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

Example

2*2*(2*2 - 1) - 1 = 11, twin prime of 13, so a(1)=2.

Maple

A200778 := 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:
end proc:
seq(A200778(n), n=1..80) ; # R. J. Mathar, Nov 26 2011

Mathematica

lktpp[n_]:=Module[{k=1, p=Prime[n]}, While[AnyTrue[k*p(k*p-1)+{1, -1}, CompositeQ], k++]; k]; Array[lktpp, 70] (* Harvey P. Dale, May 03 2019 *)

Crossrefs

Cf. A200654.

Sequence in context: A222481 A351954 A353577 * A345355 A132601 A047818

Adjacent sequences: A200775 A200776 A200777 * A200779 A200780 A200781

Keyword

nonn

Author

Pierre CAMI, Nov 22 2011

Status

approved