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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.)