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

4,2

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

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

Prog

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

Crossrefs

Cf. A191619, A191620, A205322.

Sequence in context: A070404 A258370 A135537 * A335863 A112545 A021934

Adjacent sequences: A212035 A212036 A212037 * A212039 A212040 A212041

Keyword

nonn

Author

Pierre CAMI, Jul 14 2012

Status

approved