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

1,2

Comments

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

Links

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

Formula

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

Maple

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

Prog

(PFGW64 and SCRIPTIFY)
SCRIPT
DIM nn, 0
DIM kk
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
IF nn>825 THEN END
SET kk, -1
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
PRP (2^nn+kk)*2^nn+1, tt
IF ISPRP THEN GOTO d
IF ISPRIME THEN GOTO d
GOTO loopk
LABEL d
WRITE myfile, tt
GOTO loopn
Results in a(n).txt file
all kk values such that (2^nn+kk)*2^nn-1 is prime in pfgw-primes.log and pfgw.log files

Crossrefs

Cf. A191617, A191618, A205322

Sequence in context: A317845 A278599 A281036 * A270838 A038585 A083768

Adjacent sequences: A205318 A205319 A205320 * A205322 A205323 A205324

Keyword

nonn

Author

Pierre CAMI, Jul 14 2012

Status

approved