A214495 - OEIS

%I #14 Sep 05 2012 12:11:15

%S 1,1,11,19,7,1,23,31,53,49,47,139,49,101,97,399,87,281,37,329,893,497,

%T 203,883,213,1171,633,593,1747,349,3843,479,2347,329,1921,1299,2933,

%U 1467,3097,1943,1509,2077,2111,723,2913,2307,963,361,297,1249,1031,2153

%N Smallest k>0 such that (3^n-k)*3^n-1 and (3^n-k)*3^n+1 are a twin prime pair.

%C Conjecture : there is always one such k(n) for each n>0.

%C Heuristically, as N increases, the average of a(n)/n^2 over n=1 to N tends to 1.2

%H Pierre CAMI, <a href="/A214495/b214495.txt">Table of n, a(n) for n = 1..500</a>

%p A214495 := proc(n)

%p     local k;

%p     for k from 1 do

%p         p := (3^n-k)*3^n-1 ;

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

%p             return k;

%p         end if;

%p     end do:

%p end proc: # _R. J. Mathar_, Jul 23 2012

%t sk[n_]:=Module[{k=1,n3=3^n},While[!PrimeQ[(n3-k)*n3-1]||!PrimeQ[(n3-k)* n3+1], k++];k]; Array[sk,60] (* _Harvey P. Dale_, Sep 05 2012 *)

%o (PFGW64 and SCRIPTIFY)

%o SCRIPT

%o DIM nn,0

%o DIM kk

%o DIM jj

%o DIMS tt

%o OPENFILEOUT myfile,a(n).txt

%o OPENFILEOUT myf,b(n).txt

%o LABEL loopn

%o SET nn,nn+1

%o SET jj,0

%o IF nn>500 THEN END

%o SET kk,-1

%o LABEL loopk

%o SET kk,kk+1

%o SETS tt,%d,%d\,;nn;kk

%o PRP (3^nn-kk)*3^nn-1,tt

%o IF ISPRP THEN GOTO a

%o IF ISPRIME THEN GOTO a

%o GOTO loopk

%o LABEL a

%o SET jj,jj+1

%o PRP (3^nn-kk)*3^nn+1,tt

%o IF ISPRP THEN GOTO d

%o IF ISPRIME THEN GOTO d

%o GOTO loopk

%o LABEL d

%o WRITE myfile,tt

%o SETS tt,%d,%d\,;nn;jj

%o WRITE myf,tt

%o GOTO loopn

%Y Cf. A214496.

%K nonn

%O 1,3

%A _Pierre CAMI_, Jul 19 2012