The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A214497 Smallest k>=0 such that (3^n-k)*2^n-1 and (3^n-k)*2^n+1 are a twin prime pair. 4
 0, 6, 3, 9, 9, 6, 3, 93, 3, 54, 18, 96, 213, 297, 1206, 258, 312, 201, 261, 1206, 1158, 396, 1062, 216, 708, 762, 816, 678, 3579, 762, 831, 2106, 4734, 576, 333, 633, 213, 2766, 363, 2454, 1464, 2007, 4551, 3183, 1497, 4899, 198, 66, 9984, 2847, 276, 3051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture : there is always one such k for each n>0. As N increases, the average of a(n)/n^2 over n=1 to N appears to approach 1.1 LINKS Pierre CAMI, Table of n, a(n) for n = 1..500 MAPLE A214497 := proc(n) local k; for k from 0 do p := (3^n-k)*2^n-1 ; if isprime(p) and isprime(p+2) then return k; end if; end do: end proc: seq(A214497(n), n=1..80) ; # R. J. Mathar, Jul 23 2012 MATHEMATICA sk[n_]:=Module[{k=0, c}, c=(3^n-k)2^n; While[!PrimeQ[c-1] || !PrimeQ[c+1], k++; c=(3^n-k)2^n]; k]; Array[sk, 60] (* Harvey P. Dale, Dec 09 2012 *) PROG (PFGW64 and SCRIPTIFY) 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+1 SETS tt, %d, %d\,; nn; kk PRP (3^nn-kk)*2^nn-1, tt IF ISPRP THEN GOTO a IF ISPRIME THEN GOTO a GOTO loopk LABEL a SET jj, jj+1 PRP (3^nn-kk)*2^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 CROSSREFS Cf. A214495-A214498. Sequence in context: A180596 A154465 A176533 * A177015 A355971 A327000 Adjacent sequences: A214494 A214495 A214496 * A214498 A214499 A214500 KEYWORD nonn AUTHOR Pierre CAMI, Jul 20 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)