A139638 Least number k such that k*p(n)*(k*p(n)+1)-1, k*p(n)*(k*p(n)+1)+1, k*p(n)*(k*p(n)+3)-1 and k*p(n)*(k*p(n)+3)+1 are all primes, two pairs of twin primes, with p(i) = i-th prime.

312, 1, 3, 195, 45, 48, 4884, 732, 3525, 570, 1230, 2244, 930, 15555, 660, 6513, 4656, 228, 2847, 180, 2613, 21, 18, 1176, 2832, 63, 3168, 4500, 12, 4740, 225, 465, 4602, 5940, 25575, 38799, 6939, 4821, 2067, 81, 21090, 9570, 18480, 558, 15762, 34836

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

1*3*(1*3+1)-1=11, 11 and 13 twin primes
1*3*(1*3+3)-1=17, 17 and 19 twin primes so k(2)=1 as p(2)=3

Mathematica

lnk[p_]:=Module[{k=1}, While[Total[Boole[PrimeQ[{k*p(k*p+1)-1, k*p(k*p+1)+1, k*p(k*p+3)-1, k*p(k*p+3)+1}]]]!=4, k++]; k]; Table[lnk[p], {p, Prime[ Range[ 50]]}] (* Harvey P. Dale, Jun 05 2021 *)

Crossrefs

Sequence in context: A213814 A305546 A071644 * A308002 A112542 A238099

Adjacent sequences: A139635 A139636 A139637 * A139639 A139640 A139641

Keyword

nonn

Author

Pierre CAMI, Apr 28 2008

Status

approved