A207459 - OEIS

%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