A112746 Least k such that 6*k*prime(n)^2 - 1 and 6*k*prime(n)^2 + 1 are twin primes.

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

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 A353298 A152975

Adjacent sequences: A112743 A112744 A112745 * A112747 A112748 A112749

Keyword

nonn

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