A048630 n-th 4k+1 prime times n-th 4k-1 prime.

15, 91, 187, 551, 851, 1271, 2279, 2867, 4307, 5963, 6887, 7979, 9047, 11639, 14659, 18923, 20567, 24047, 27331, 31459, 32899, 40991, 44503, 47959, 54227, 59987, 62879, 67159, 73543, 82319, 85907, 95371, 107143, 109783, 123463, 134983, 142523, 147167, 155011

Offset

1,1

Comments

Together with {2} gives the primitive elements of A354192. - Antti Karttunen, May 20 2022

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A002144(n) * A002145(n).

a(n) = A267099(a(n)). - Antti Karttunen, May 20 2022

Maple

P1:= select(isprime, [seq(i, i=1..1000, 4)]):
P2:= select(isprime, [seq(i, i=3..1000, 4)]):
zip(`*`, P1, P2); # Robert Israel, Jan 21 2020

Mathematica

zip[f_, x_, y_, z_] := With[{m = Max[Length[x],
   Length[y]]}, f[PadRight[x, m, z], PadRight[y, m, z]]];
zip[Times,
   Select[Range[1, 1000, 4], PrimeQ],
   Select[Range[3, 1000, 4], PrimeQ], 0] //
   Select[#, Positive]& (* Jean-François Alcover, Dec 05 2023 *)

Prog

(PARI) m=35; nm=0; np=0; pm=vector(m); pp=vector(m);
forstep(k=4, oo, 4, if(nm<m&&isprime(k-1), pm[nm++]=k-1); if(np<m&&isprime(k+1), pp[np++]=k+1); if(min(nm, np)==m, break));
for(j=1, m, print1(pm[j]*pp[j], ", ")) \\ Hugo Pfoertner, Jan 21 2020
(Magma) m:=95; v:=[4*k-1: k in [1..m]|IsPrime(4*k-1)]; w:=[4*k+1: k in  [1..m]|IsPrime(4*k+1)]; [v[k]*w[k]:k in [1..Min([#v, #w])]]; // Marius A. Burtea, Jan 21 2020

Crossrefs

Cf. A002144, A002145, A048628, A267099, A354192.

Subsequence of A001358 and of A080774.

Sequence in context: A263629 A320524 A218408 * A326148 A035163 A237516

Adjacent sequences: A048627 A048628 A048629 * A048631 A048632 A048633

Keyword

nonn

Author

N. J. A. Sloane, Den Roussel (DenRoussel(AT)webtv.net)

Extensions

Offset corrected by Robert Israel, Jan 21 2020

Status

approved