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%I #16 Jul 23 2012 17:01:50
%S 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 62,20,31,23,28,30,14,47,22,10,5,104,39,11,14,64,184,209,176,193,162,
%U 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 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 Search set similar to A212037 but the sign of k in the prime form is switched.
%C Heuristically the average of a(n)/n for n=1 to N tends to 1 as N increases.
%H Pierre CAMI, <a href="/A212038/b212038.txt">Table of n, a(n) for n = 4..825</a>
%p A212038 := proc(n)
%p local a,k,p ;
%p a := 0 ;
%p for k from 0 do
%p p := (2^n-k)*2^n-1 ;
%p if isprime(p) then
%p a := a+1 ;
%p end if;
%p if isprime(p) and isprime(p+2) then
%p return a;
%p end if;
%p end do:
%p end proc: # _R. J. Mathar_, Jul 21 2012
%o SCRIPT
%o DIM nn, 3
%o DIM jj
%o DIM kk
%o DIMS tt
%o OPENFILEOUT myfile, a(n).txt
%o LABEL loopn
%o SET nn, nn+1
%o IF nn>825 THEN END
%o SET kk, -1
%o SET jj, 0
%o LABEL loopk
%o SET kk, kk+1
%o SETS tt, %d, %d\,; nn; kk
%o PRP (2^nn-kk)*2^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 (2^nn-kk)*2^nn+1, tt
%o IF ISPRP THEN GOTO d
%o IF ISPRIME THEN GOTO d
%o GOTO loopk
%o LABEL d
%o SETS tt, %d, %d\,; nn; jj
%o WRITE myfile, tt
%o GOTO loopn
%Y Cf. A191619, A191620, A205322.
%K nonn
%O 4,2
%A _Pierre CAMI_, Jul 14 2012
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