A211162 Sophie Germain 5-almost primes.

688, 1552, 3496, 4360, 5008, 6352, 6952, 7546, 7672, 9256, 9625, 9712, 10062, 10300, 10840, 11632, 11875, 12112, 12136, 12460, 12712, 13432, 13648, 13744, 13912, 14152, 14812, 14920, 15484, 16562, 17050, 17104, 17272, 17608, 17752, 18130, 18232, 18616, 18952, 19062, 19624, 19792, 21100, 21136, 21352

Offset

1,1

Comments

Numbers n that are products of exactly 5 primes, such that 2*n + 1 are also products of exactly 5 primes. By analogy with A111153 Sophie Germain semiprimes: semiprimes n such that 2n+1 is also a semiprime; A111173 Sophie Germain 3-almost primes; A111176 Sophie Germain 4-almost primes.

From Zak Seidov, Jan 30 2013: (Start)

First integers n such that both n and 2n+1 are Sophie Germain 5-almost primes are: 54708, 103812, 111952, 113368, 117328, 134312, 159568, 160062, 165462, 199048, 205812.

First integers n such that n, 2n+1 and 4n+3 all are Sophie Germain 5-almost primes are: 159568, 301812, 431068, 444388, 564718, 1144468, 1420468, 1653162, 1687768, 1794568.

First integers n such that n, 2n+1, 4n+3 and 8n+7 all are Sophie Germain 5-almost primes are: 2991345, 4553367, 7760616, 9145318, 9332368, 12919266, 14283535, 14659746, 15144118.

First integers n such that n, 2n+1, 4n+3, 8n+7 and 16n+15 all are Sophie Germain 5-almost primes are: 15144118, 18515752, 41092024, 60406662, 71783890, 87353512, 94144212

First integers n such that n, 2n+1, 4n+3, 8n+7, 16n+15 and 32n+31 all are Sophie Germain 5-almost primes are: 211457337, 237572475, 245071092, 352015408, 415695462, 433833417.

First integers n such that n, 2n+1, 4n+3, 8n+7, 16n+15, 32n+31 and 64n+63 all are Sophie Germain 5-almost primes are: 433833417, 463078210, 648871975. (End)

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Formula

{n in A014614 such that 2*n + 1 is in A014614}.

Example

a(1) = 688 because 688 = 2^4 * 43, and 2*688 + 1 = 1377 = 3^4 * 17.

Mathematica

fQ[n_] := PrimeOmega[n] == 5 == PrimeOmega[2 n + 1]; Select[Range@ 100000, fQ] (* Robert G. Wilson v *)

Prog

(Magma) Is5primes:=func<i|&+[d[2]: d in Factorization(i)] eq 5>; [n: n in [2..22000] | Is5primes(n) and Is5primes(2*n+1)]; // Bruno Berselli, Jan 30 2013
(PARI) is(n)=bigomega(n)==5 && bigomega(2*n+1)==5 \\ Charles R Greathouse IV, Feb 01 2017

Crossrefs

Cf. A014614, A111153, A111173, A111176.

Sequence in context: A296811 A252642 A252084 * A235851 A057116 A025355

Adjacent sequences: A211159 A211160 A211161 * A211163 A211164 A211165

Keyword

nonn

Author

Jonathan Vos Post and Robert G. Wilson v, Jan 30 2013

Status

approved