A104006 - OEIS

%I #16 Apr 21 2019 13:55:35

%S 19,31,43,67,71,79,103,131,139,191,223,239,283,311,367,419,431,439,

%T 443,499,599,607,619,643,647,659,683,743,787,823,827,907,947,971,1031,

%U 1039,1087,1091,1103,1163,1223,1259,1399,1427,1447,1499,1511,1543,1559,1571

%N Primes of the form 2pq + 1, where p and q are (not necessarily distinct) odd primes.

%H T. D. Noe, <a href="/A104006/b104006.txt">Table of n, a(n) for n=1..1000</a>

%e 19 = 2*3*3 + 1.

%e 31 = 2*3*5 + 1.

%t Select[Prime[Range[3, 500]], FactorInteger[(# - 1)/2][[1, 1]] > 2 && Sum[FactorInteger[(# - 1)/2][[i, 2]], {i, 1, Length[FactorInteger[(# - 1)/2]]}] == 2 &] (* _Stefan Steinerberger_, Sep 26 2007 *)

%t Take[ Select[ Sort[ Flatten[ Table[ 2Prime[p]Prime[q] + 1, {p, 47}, {q, p}]]], PrimeQ[ # ] &], 50] (* _Robert G. Wilson v_, Apr 06 2005 *)

%t Select[Prime[Range[19,500]], OddQ[ (#-1)/2]&&3==Plus@@Last/@FactorInteger[ #-1]&] (* _Zak Seidov_, Sep 26 2007 *)

%t With[{upto=Prime[250]},Select[2#[[1]]#[[2]]+1&/@Tuples[Prime[Range[2, upto/6]],2],PrimeQ[#]&&#<=upto&]]//Union (* _Harvey P. Dale_, Apr 21 2019 *)

%K easy,nonn

%O 1,1

%A _Giovanni Teofilatto_, Mar 31 2005

%E Edited, corrected and extended by _Robert G. Wilson v_, Apr 06 2005