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%I #18 Mar 07 2013 11:08:10
%S 3,5,7,12,13,18,27,28,43,47,58,133,168,170,192,195,223,230,308,348,
%T 365,370,373,385,417,443,468,532,737,742,875,917,1043,1050,1063,1148,
%U 1160,1170,1257,1390,1435,1440,1518,1547,1587,1612,1617,1690,1700,1725
%N a(n) is the least number > a(n-1) such that 6*a(n)*prime(n)^2 - 1 and 6*a(n)*prime(n)^2 + 1 are twin primes.
%C As n increases, a(n)/(n*(log(P(n))^2)) is always near 1.200.
%H Pierre CAMI, <a href="/A207459/b207459.txt">Table of n, a(n) for n = 1..10000</a>
%e 6*3*2^2-1=71 , 71 and 73 twin primes so a(1)=3 as prime(1)=2.
%e 6*5*3^2-1=269 269 and 271 twin primes so a(2)=5 as prime(2)=3.
%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,0
%o DIMS tt
%o OPENFILEOUT myfile,values.txt
%o LABEL loopn
%o SET nn,nn+1
%o IF nn>50000 THEN END
%o LABEL loopk
%o SET kk,kk+1
%o SETS tt,%d,%d\ ;nn;kk
%o PRP 6*kk*p(nn)^2-1,tt
%o IF ISPRP THEN GOTO a
%o IF ISPRIME THEN GOTO a
%o GOTO loopk
%o LABEL a
%o PRP 6*kk*p(nn)^2+1,tt
%o IF ISPRP THEN GOTO b
%o IF ISPRIME THEN GOTO b
%o GOTO loopk
%o LABEL b
%o WRITE myfile,tt
%o GOTO loopn
%Y Cf. A112746.
%K nonn
%O 1,1
%A _Pierre CAMI_, Feb 18 2012
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