A212487 Smallest k > 0 such that (5^n+k)*5^n-1 and (5^n+k)*5^n+1 are a twin prime pair.

1, 17, 85, 47, 19, 71, 955, 815, 223, 269, 607, 1619, 2737, 53, 883, 1319, 2797, 4757, 1585, 1535, 295, 557, 3511, 269, 277, 5747, 2125, 53, 13345, 2195, 109, 1175, 2995, 5597, 3787, 1619, 6577, 8549, 3475, 5435, 4807, 20045, 23353, 9341, 2857, 2117, 1429, 16283, 25333, 7949

Offset

1,2

Comments

Conjecture: there is always one such k for n > 0.

Links

Pierre CAMI, Table of n, a(n) for n = 1..500

Formula

a(n) = A082466(5^n). - R. J. Mathar, Jul 20 2012

Maple

A212487 := proc(n)
    local k, p ;
    for k from 1 do
        p := (5^n+k)*5^n-1 ;
        if isprime(p) and isprime(p+2) then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 20 2012

Prog

SCRIPT
DIM nn, 0
DIM kk
DIM jj
DIMS tt
OPENFILEOUT myfile, a(n).txt
OPENFILEOUT myf, b(n).txt
LABEL loopn
SET nn, nn+1
SET jj, 0
IF nn>500 THEN END
SET kk, -1
LABEL loopk
SET kk, kk+2
SETS tt, %d, %d\,; nn; kk
PRP (5^nn+kk)*5^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
SET jj, jj+1
PRP (5^nn+kk)*5^nn+1, tt
IF ISPRP THEN GOTO d
IF ISPRIME THEN GOTO d
GOTO loopk
LABEL d
WRITE myfile, tt
SETS tt, %d, %d\,; nn; jj
WRITE myf, tt
GOTO loopn

Crossrefs

Cf. A212488.

Sequence in context: A239667 A344523 A156968 * A288420 A156157 A146389

Adjacent sequences: A212484 A212485 A212486 * A212488 A212489 A212490

Keyword

nonn

Author

Pierre CAMI, Jul 18 2012

Status

approved