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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 (list; graph; refs; listen; history; text; internal format)
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 * A241515 A070334 A137700

Adjacent sequences:  A207456 A207457 A207458 * A207460 A207461 A207462

KEYWORD

nonn

AUTHOR

Pierre CAMI, Feb 18 2012

STATUS

approved

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Last modified May 16 11:35 EDT 2022. Contains 353704 sequences. (Running on oeis4.)