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%I #10 Jul 20 2012 13:23:25
%S 0,11,1,11,4,11,13,116,34,14,241,44,97,458,337,59,604,206,67,167,424,
%T 179,97,326,259,284,1177,77,328,356,508,74,1798,749,2197,1289,643,839,
%U 1171,1427,814,2564,31,4244,379,5099,3706,4871,2719,3194,7057,122,5329,2636,301,2852,3793
%N Smallest k>=0 such that (2^n+k)*2^n-1 and (2^n+k)*2^n+1 are a twin prime pair.
%C Conjecture : there is at least one k for each n.
%H Pierre CAMI, <a href="/A205321/b205321.txt">Table of n, a(n) for n = 1..825</a>
%F a(n) = A082466(2^n), n>1. - _R. J. Mathar_, Jul 20 2012
%p A205321 := proc(n)
%p local a,p ;
%p for a from 0 do
%p p := (2^n+a)*2^n-1 ;
%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 18 2012
%o (PFGW64 and SCRIPTIFY)
%o SCRIPT
%o DIM nn,0
%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 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 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 WRITE myfile,tt
%o GOTO loopn
%o Results in a(n).txt file
%o all kk values such that (2^nn+kk)*2^nn-1 is prime in pfgw-primes.log and pfgw.log files
%Y Cf. A191617, A191618, A205322
%K nonn
%O 1,2
%A _Pierre CAMI_, Jul 14 2012
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