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A112746 Least k such that 6*k*prime(n)^2 - 1 and 6*k*prime(n)^2 + 1 are twin primes. 4
3, 2, 1, 3, 2, 2, 2, 20, 22, 2, 12, 10, 28, 32, 8, 7, 20, 15, 15, 12, 5, 3, 68, 15, 33, 12, 10, 3, 23, 28, 130, 8, 13, 32, 38, 7, 57, 3, 25, 3, 8, 18, 77, 12, 65, 22, 18, 18, 2, 10, 18, 30, 110, 10, 10, 28, 15, 22, 37, 7, 2, 10, 7, 8, 48, 3, 3, 87, 103, 128, 30 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Define Sp sum of log(6*prime(n))^2 from n=1 to N. Define Sk sum of k from n=1 to N. As N increases Sk/Sp tends to 0.6.

LINKS

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

EXAMPLE

6*1*prime(1)^2-1=23 prime but 25 composite.

6*2*prime(1)^2-1=47 prime but 49 composite.

6*3*prime(1)^2-1=71 prime as 73 so a(1)=3.

MATHEMATICA

Table[k = 1; While[c = 6*k*Prime[n]^2; ! PrimeQ[c - 1] || ! PrimeQ[c + 1], k++ ]; k, {n, 80}] (* Ray Chandler, Oct 08 2005 *)

PROG

(PFGW64 from Primeform group and SCRIPTIFY)

Command pfgw64 -f in.txt

in.txt file :

SCRIPT

DIM nn, 0

DIM kk

DIMS tt

OPENFILEOUT myfile, twin.txt

LABEL loopn

SET nn, nn+1

IF nn>10000 THEN END

SET kk, 0

LABEL loopk

SET kk, kk+1

SETS tt, %d, %d\,; p(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. A112744, A112745.

Sequence in context: A138034 A229216 A087818 * A107460 A152975 A244758

Adjacent sequences:  A112743 A112744 A112745 * A112747 A112748 A112749

KEYWORD

nonn,changed

AUTHOR

Pierre CAMI, Sep 18 2005

EXTENSIONS

Extended by Ray Chandler, Oct 08 2005

Corrected, extended and b file by Pierre CAMI, Feb 27 2012

STATUS

approved

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Last modified September 21 22:07 EDT 2019. Contains 327283 sequences. (Running on oeis4.)