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%I #16 Aug 03 2014 14:01:39
%S 1,2,3,4,6,7,9,15,24,27,28,33,34,35,58,60,61,65,67,68,69,74,78,81,86,
%T 91,92,96,105,106,108,110,119,121,125,128,129,133,134,135,137,138,146,
%U 155,172,173,174,177,179,187,199,215,216,224
%N Numbers n such that 3*prime(n)*2^k - 1 is prime for some k > 0 and then 3*prime(n)*2^k + 1 is also prime.
%C Note that only first k for which 3*prime(n)*2^k - 1 is prime is used to test whether 3*prime(n)*2^k + 1 is prime.
%H Pierre CAMI, <a href="/A208281/b208281.txt">Table of n, a(n) for n = 1..6836</a>
%e 3*prime(1)*2^1-1=11 prime,13 prime so a(1)=1
%e 3*prime(2)*2^1-1=17 prime,19 prime so a(2)=2
%e 3*prime(3)*2^1-1=29 prime,31 prime so a(3)=3
%e 3*prime(4)*2^1-1=41 prime,43 prime so a(4)=4
%e 3*prime(5)*2^1-1=65 composite
%e 3*prime(5)*2^2-1=131 prime,133 composite
%e 3*prime(6)*2^1-1=77 composite
%e 3*prime(6)*2^2-1=155 composite
%e 3*prime(6)*2^3-1=311 prime,313 prime so a(5)=6
%t t = {}; Do[p = Prime[n]; k = 1; While[! PrimeQ[3*p*2^k - 1], k++]; If[PrimeQ[3*p*2^k + 1], AppendTo[t, n]], {n, 224}]; t (* _T. D. Noe_, Feb 29 2012 *)
%o PFGW64 from Primeform group and SCRIPTIFY
%o Command pfgw64 -f in.txt
%o in.txt file :
%o SCRIPT
%o DIM nn,0
%o DIM kk
%o DIMS tt
%o OPENFILEOUT myfile,k.txt
%o LABEL loopn
%o SET nn,nn+1
%o IF nn>50000 THEN END
%o SET kk,0
%o LABEL loopk
%o SET kk,kk+1
%o SETS tt,%d,%d\,;nn;kk
%o PRP 3*p(nn)*2^kk-1,tt
%o IF ISPRP THEN GOTO a
%o IF ISPRIME THEN GOTO a
%o GOTO loopk
%o LABEL a
%o PRP 3*p(nn)*2^kk+1,tt
%o IF ISPRP THEN GOTO b
%o IF ISPRIME THEN GOTO b
%o GOTO loopn
%o LABEL b
%o WRITE myfile,tt
%o GOTO loopn
%Y Cf. A207572.
%K nonn
%O 1,2
%A _Pierre CAMI_, Feb 25 2012
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