A082466 -id:A082466 - cp's OEIS frontend

A205321 Smallest k>=0 such that (2^n+k)2^n-1 and (2^n+k)2^n+1 are a twin prime pair.

0, 11, 1, 11, 4, 11, 13, 116, 34, 14, 241, 44, 97, 458, 337, 59, 604, 206, 67, 167, 424, 179, 97, 326, 259, 284, 1177, 77, 328, 356, 508, 74, 1798, 749, 2197, 1289, 643, 839, 1171, 1427, 814, 2564, 31, 4244, 379, 5099, 3706, 4871, 2719, 3194, 7057, 122, 5329, 2636, 301, 2852, 3793

Offset: 1

Pierre CAMI, Jul 14 2012

nonn

Conjecture : there is at least one k for each n.

Pierre CAMI, Table of n, a(n) for n = 1..825

Cf. A191617, A191618, A205322

A205321 := proc(n)
    local a,p ;
    for a from 0 do
         p := (2^n+a)*2^n-1 ;
        if isprime(p) and isprime(p+2) then
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 18 2012

a(n) = A082466(2^n), n>1. - R. J. Mathar, Jul 20 2012

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

Original entry on oeis.org

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

Pierre CAMI, Jul 18 2012

nonn

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

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

Cf. A212488.

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

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

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

cp's OEIS Frontend

A205321 Smallest k>=0 such that (2^n+k)2^n-1 and (2^n+k)2^n+1 are a twin prime pair.

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

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cp's OEIS Frontend

A205321 Smallest k>=0 such that (2^n+k)*2^n-1 and (2^n+k)*2^n+1 are a twin prime pair.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

PFGW

Formula

A205321 Smallest k>=0 such that (2^n+k)2^n-1 and (2^n+k)2^n+1 are a twin prime pair.

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