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A104006
Primes of the form 2pq + 1, where p and q are (not necessarily distinct) odd primes.
1
19, 31, 43, 67, 71, 79, 103, 131, 139, 191, 223, 239, 283, 311, 367, 419, 431, 439, 443, 499, 599, 607, 619, 643, 647, 659, 683, 743, 787, 823, 827, 907, 947, 971, 1031, 1039, 1087, 1091, 1103, 1163, 1223, 1259, 1399, 1427, 1447, 1499, 1511, 1543, 1559, 1571
OFFSET
1,1
EXAMPLE
19 = 2*3*3 + 1.
31 = 2*3*5 + 1.
MATHEMATICA
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 *)
Take[ Select[ Sort[ Flatten[ Table[ 2Prime[p]Prime[q] + 1, {p, 47}, {q, p}]]], PrimeQ[ # ] &], 50] (* Robert G. Wilson v, Apr 06 2005 *)
Select[Prime[Range[19, 500]], OddQ[ (#-1)/2]&&3==Plus@@Last/@FactorInteger[ #-1]&] (* Zak Seidov, Sep 26 2007 *)
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 *)
CROSSREFS
Sequence in context: A286313 A040068 A096787 * A117065 A006035 A104485
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Mar 31 2005
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Apr 06 2005
STATUS
approved