This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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