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A211162 Sophie Germain 5-almost primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 14:08 EDT 2021. Contains 347617 sequences. (Running on oeis4.)