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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

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

Adjacent sequences:  A104003 A104004 A104005 * A104007 A104008 A104009

KEYWORD

easy,nonn

AUTHOR

Giovanni Teofilatto, Mar 31 2005

EXTENSIONS

Edited, corrected and extended by Robert G. Wilson v, Apr 06 2005

STATUS

approved

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)