A111351 - OEIS

A111351

Semiprimes of the form 2*n + 1, where n is a square.

9, 33, 51, 129, 201, 289, 339, 393, 451, 579, 649, 723, 1059, 1569, 1923, 2049, 3043, 3873, 4609, 4803, 5001, 5619, 5833, 6051, 6499, 6729, 7201, 7939, 8193, 9249, 9523, 10083, 11553, 12169, 13123, 13449, 14113, 14451, 14793, 15843, 16201, 16563

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OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = 2*A111350(n) + 1.

MATHEMATICA

Select[2Range[100]^2 + 1, Plus @@ Last /@ FactorInteger[ # ] == 2 &] (* Ray Chandler, Nov 10 2005 *)

Select[2*Range[100]^2+1, PrimeOmega[#]==2&] (* Harvey P. Dale, May 07 2013 *)

PROG

(Magma) IsSemiprime:=func<t | &+[d[2]: d in Factorization(t)] eq 2>; [s: t in [2..100] | IsSemiprime(s) where s is 2*t^2 + 1]; // Bruno Berselli, Sep 22 2012

CROSSREFS

Cf. A111350, A112777.

Sequence in context: A020226 A175440 A280405 * A065064 A337234 A075812

Adjacent sequences: A111348 A111349 A111350 * A111352 A111353 A111354

KEYWORD

nonn,easy

AUTHOR

Giovanni Teofilatto, Oct 29 2005

EXTENSIONS

Edited and extended by Ray Chandler, Nov 10 2005

Offset corrected by Arkadiusz Wesolowski, Aug 09 2011

STATUS

approved