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A214496 Smallest k>0 such that (3^n+k)*3^n-1 and (3^n+k)*3^n+1 are a twin prime pair.

%I A214496 #15 Mar 08 2013 03:35:31
%S A214496 1,3,3,7,21,29,113,31,61,13,179,237,33,201,613,171,347,291,907,437,
%T A214496 523,193,1039,729,567,231,1847,931,1023,821,329,3937,6137,319,1663,
%U A214496 667,1837,529,1769,1959,1781,743,3223,591,613,473,5679,2137,567,459,4729
%N A214496 Smallest k>0 such that (3^n+k)*3^n-1 and (3^n+k)*3^n+1 are a twin prime pair.
%C A214496 Conjecture : there is always one such k for each n>0.
%C A214496 Heuristically, as N increases, the average of a(n)/n^2 for n=1 to N tends to 1.2
%H A214496 Pierre CAMI, <a href="/A214496/b214496.txt">Table of n, a(n) for n = 1..500</a>
%p A214496 A214496 := proc(n)
%p A214496     local k;
%p A214496     for k from 1 do
%p A214496         p := (3^n+k)*3^n-1 ;
%p A214496         if isprime(p) and isprime(p+2) then
%p A214496             return k;
%p A214496         end if;
%p A214496     end do:
%p A214496 end proc: # _R. J. Mathar_, Jul 23 2012
%o A214496 (PFGW64 and SCRIPTIFY)
%o A214496 SCRIPT
%o A214496 DIM nn,0
%o A214496 DIM kk
%o A214496 DIM jj
%o A214496 DIMS tt
%o A214496 OPENFILEOUT myfile,a(n).txt
%o A214496 OPENFILEOUT myf,b(n).txt
%o A214496 LABEL loopn
%o A214496 SET nn,nn+1
%o A214496 SET jj,0
%o A214496 IF nn>500 THEN END
%o A214496 SET kk,-1
%o A214496 LABEL loopk
%o A214496 SET kk,kk+1
%o A214496 SETS tt,%d,%d\,;nn;kk
%o A214496 PRP (3^nn+kk)*3^nn-1,tt
%o A214496 IF ISPRP THEN GOTO a
%o A214496 IF ISPRIME THEN GOTO a
%o A214496 GOTO loopk
%o A214496 LABEL a
%o A214496 SET jj,jj+1
%o A214496 PRP (3^nn+kk)*3^nn+1,tt
%o A214496 IF ISPRP THEN GOTO d
%o A214496 IF ISPRIME THEN GOTO d
%o A214496 GOTO loopk
%o A214496 LABEL d
%o A214496 WRITE myfile,tt
%o A214496 SETS tt,%d,%d\,;nn;jj
%o A214496 WRITE myf,tt
%o A214496 GOTO loopn
%Y A214496 Cf. A214495.
%K A214496 nonn
%O A214496 1,2
%A A214496 _Pierre CAMI_, Jul 20 2012