cp's OEIS Frontend

A212038 The size of the set of numbers k>=0 such that all (2^n-k)*2^n-1 are prime but only (2^n-k)*2^n+1 with the largest k is also the associated twin prime.

%I A212038 #19 Sep 03 2024 15:14:07
%S A212038 1,7,5,2,4,11,6,1,3,2,31,2,11,11,11,6,30,16,2,36,90,56,11,52,13,36,10,
%T A212038 62,20,31,23,28,30,14,47,22,10,5,104,39,11,14,64,184,209,176,193,162,
%U A212038 25,38,23,5,27,157,5,17,32,90,1,199,96,83,29,82,12,220,19,40,37,13,16,120,11,130,12,77,202
%N A212038 The size of the set of numbers k>=0 such that all (2^n-k)*2^n-1 are prime but only (2^n-k)*2^n+1 with the largest k is also the associated twin prime.
%C A212038 Search set similar to A212037 but the sign of k in the prime form is switched.
%C A212038 Heuristically the average of a(n)/n for n=1 to N tends to 1 as N increases.
%H A212038 Pierre CAMI, <a href="/A212038/b212038.txt">Table of n, a(n) for n = 4..825</a>
%p A212038 A212038 := proc(n)
%p A212038     local a,k,p ;
%p A212038     a := 0 ;
%p A212038     for k from 0 do
%p A212038         p := (2^n-k)*2^n-1 ;
%p A212038         if isprime(p) then
%p A212038             a := a+1 ;
%p A212038         end if;
%p A212038         if isprime(p) and isprime(p+2) then
%p A212038             return a;
%p A212038         end if;
%p A212038     end do:
%p A212038 end proc: # _R. J. Mathar_, Jul 21 2012
%o A212038 (PFGW)
%o A212038 SCRIPT
%o A212038 DIM nn, 3
%o A212038 DIM jj
%o A212038 DIM kk
%o A212038 DIMS tt
%o A212038 OPENFILEOUT myfile, a(n).txt
%o A212038 LABEL loopn
%o A212038 SET nn, nn+1
%o A212038 IF nn>825 THEN END
%o A212038 SET kk, -1
%o A212038 SET jj, 0
%o A212038 LABEL loopk
%o A212038 SET kk, kk+1
%o A212038 SETS tt, %d, %d\,; nn; kk
%o A212038 PRP (2^nn-kk)*2^nn-1, tt
%o A212038 IF ISPRP THEN GOTO a
%o A212038 IF ISPRIME THEN GOTO a
%o A212038 GOTO loopk
%o A212038 LABEL a
%o A212038 SET jj, jj+1
%o A212038 PRP (2^nn-kk)*2^nn+1, tt
%o A212038 IF ISPRP THEN GOTO d
%o A212038 IF ISPRIME THEN GOTO d
%o A212038 GOTO loopk
%o A212038 LABEL d
%o A212038 SETS tt, %d, %d\,; nn; jj
%o A212038 WRITE myfile, tt
%o A212038 GOTO loopn
%Y A212038 Cf. A191619, A191620, A205322.
%K A212038 nonn
%O A212038 4,2
%A A212038 _Pierre CAMI_, Jul 14 2012