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

Author

Pierre CAMI, Jul 18 2012

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A212488.

Programs

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

PFGW

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

Formula

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