A212038 The size of the set of numbers k>=0 such that all (2^n-k)*2^n-1 are prime but only (2^n-k)*2^n+1 with the largest k is also the associated twin prime.

1, 7, 5, 2, 4, 11, 6, 1, 3, 2, 31, 2, 11, 11, 11, 6, 30, 16, 2, 36, 90, 56, 11, 52, 13, 36, 10, 62, 20, 31, 23, 28, 30, 14, 47, 22, 10, 5, 104, 39, 11, 14, 64, 184, 209, 176, 193, 162, 25, 38, 23, 5, 27, 157, 5, 17, 32, 90, 1, 199, 96, 83, 29, 82, 12, 220, 19, 40, 37, 13, 16, 120, 11, 130, 12, 77, 202

Offset: 4

Author

Pierre CAMI, Jul 14 2012

Keywords

• nonn

Comments

Search set similar to A212037 but the sign of k in the prime form is switched.

Heuristically the average of a(n)/n for n=1 to N tends to 1 as N increases.

Links

• Pierre CAMI, Table of n, a(n) for n = 4..825

Crossrefs

Cf. A191619, A191620, A205322.

Programs

Maple

A212038 := proc(n)
    local a,k,p ;
    a := 0 ;
    for k from 0 do
        p := (2^n-k)*2^n-1 ;
        if isprime(p) then
            a := a+1 ;
        end if;
        if isprime(p) and isprime(p+2) then
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 21 2012

PFGW

SCRIPT
DIM nn, 3
DIM jj
DIM kk
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
IF nn>825 THEN END
SET kk, -1
SET jj, 0
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP (2^nn-kk)*2^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
SET jj, jj+1
PRP (2^nn-kk)*2^nn+1, tt
IF ISPRP THEN GOTO d
IF ISPRIME THEN GOTO d
GOTO loopk
LABEL d
SETS tt, %d, %d\,; nn; jj
WRITE myfile, tt
GOTO loopn