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.

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.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A207456 A207457 A207458 * A207460 A207461 A207462

Keyword

nonn

Author

Pierre CAMI, Feb 18 2012

Status

approved