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%I #32 Dec 05 2023 19:51:20
%S 15,91,187,551,851,1271,2279,2867,4307,5963,6887,7979,9047,11639,
%T 14659,18923,20567,24047,27331,31459,32899,40991,44503,47959,54227,
%U 59987,62879,67159,73543,82319,85907,95371,107143,109783,123463,134983,142523,147167,155011
%N n-th 4k+1 prime times n-th 4k-1 prime.
%C Together with {2} gives the primitive elements of A354192. - _Antti Karttunen_, May 20 2022
%H Robert Israel, <a href="/A048630/b048630.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A002144(n) * A002145(n).
%F a(n) = A267099(a(n)). - _Antti Karttunen_, May 20 2022
%p P1:= select(isprime, [seq(i,i=1..1000,4)]):
%p P2:= select(isprime, [seq(i,i=3..1000,4)]):
%p zip(`*`,P1,P2); # _Robert Israel_, Jan 21 2020
%t zip[f_, x_, y_, z_] := With[{m = Max[Length[x],
%t Length[y]]}, f[PadRight[x, m, z], PadRight[y, m, z]]];
%t zip[Times,
%t Select[Range[1, 1000, 4], PrimeQ],
%t Select[Range[3, 1000, 4], PrimeQ], 0] //
%t Select[#, Positive]& (* _Jean-François Alcover_, Dec 05 2023 *)
%o (PARI) m=35;nm=0;np=0;pm=vector(m);pp=vector(m);
%o 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));
%o for(j=1,m,print1(pm[j]*pp[j],", ")) \\ _Hugo Pfoertner_, Jan 21 2020
%o (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
%Y Cf. A002144, A002145, A048628, A267099, A354192.
%Y Subsequence of A001358 and of A080774.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Den Roussel (DenRoussel(AT)webtv.net)
%E Offset corrected by _Robert Israel_, Jan 21 2020
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