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A207459
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.
1
3, 5, 7, 12, 13, 18, 27, 28, 43, 47, 58, 133, 168, 170, 192, 195, 223, 230, 308, 348, 365, 370, 373, 385, 417, 443, 468, 532, 737, 742, 875, 917, 1043, 1050, 1063, 1148, 1160, 1170, 1257, 1390, 1435, 1440, 1518, 1547, 1587, 1612, 1617, 1690, 1700, 1725
OFFSET
1,1
COMMENTS
As n increases, a(n)/(n*(log(P(n))^2)) is always near 1.200.
EXAMPLE
6*3*2^2-1=71 , 71 and 73 twin primes so a(1)=3 as prime(1)=2.
6*5*3^2-1=269 269 and 271 twin primes so a(2)=5 as prime(2)=3.
PROG
PFGW64 from Primeform group and Scriptify
Command : PFGW64 -f in.txt
in.txt file :
SCRIPT
DIM nn, 0
DIM kk, 0
DIMS tt
OPENFILEOUT myfile, values.txt
LABEL loopn
SET nn, nn+1
IF nn>50000 THEN END
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\ ; nn; kk
PRP 6*kk*p(nn)^2-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
PRP 6*kk*p(nn)^2+1, tt
IF ISPRP THEN GOTO b
IF ISPRIME THEN GOTO b
GOTO loopk
LABEL b
WRITE myfile, tt
GOTO loopn
CROSSREFS
Cf. A112746.
Sequence in context: A339789 A293598 A243179 * A368036 A241515 A070334
KEYWORD
nonn
AUTHOR
Pierre CAMI, Feb 18 2012
STATUS
approved