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A205322 Smallest k>=0 such that (2^n-k)*2^n-1 and (2^n-k)*2^n+1 are a twin prime pair; or -1 if no such k exists. 4
0, 1, -1, 1, 26, 22, 8, 28, 47, 16, 14, 19, 17, 316, 8, 133, 116, 166, 77, 364, 197, 49, 647, 1594, 848, 109, 869, 169, 773, 166, 1274, 466, 512, 694, 644, 733, 401, 1636, 662, 184, 71, 3106, 1157, 346, 332, 2194, 6179, 7999, 6023, 6784, 5612, 1108, 1001, 649, 197 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Conjecture: there is always at least one k>=0 unless n=3.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..826

MAPLE

A205322 := proc(n)

    local a, p ;

    for a from 0 to 2^n do

         p := (2^n-a)*2^n-1 ;

        if isprime(p) and isprime(p+2) then

            return a;

        end if;

    end do:

    return -1 ;

end proc: # R. J. Mathar, Jul 18 2012

MATHEMATICA

Table[k = -1; While[k++; p = 4^n - k*2^n - 1; p > 0 && ! (PrimeQ[p] && PrimeQ[p + 2])]; If[p <= 0, -1, k], {n, 50}] (* T. D. Noe, Mar 15 2013 *)

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==3 THEN SET nn, 4

IF nn>826 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

CROSSREFS

Cf. A191619, A191620, A205321.

Sequence in context: A154295 A277685 A072360 * A291470 A093538 A220087

Adjacent sequences:  A205319 A205320 A205321 * A205323 A205324 A205325

KEYWORD

sign

AUTHOR

Pierre CAMI, Jul 14 2012

STATUS

approved

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Last modified October 22 18:17 EDT 2019. Contains 328319 sequences. (Running on oeis4.)