A111173 Sophie Germain triprimes: k and 2k + 1 are both the product of 3 primes, not necessarily distinct.

52, 76, 130, 171, 172, 212, 238, 318, 322, 325, 332, 357, 370, 387, 388, 402, 423, 430, 436, 442, 465, 507, 508, 556, 604, 610, 654, 665, 670, 710, 722, 747, 759, 762, 772, 775, 786, 790, 805, 814, 822, 826, 847, 874, 885, 902, 906, 916, 927, 942, 987, 1004

Offset

1,1

Comments

There should also be triprime chains of length j analogous to Cunningham chains of the first kind and Tomaszewski chains of the first kind. A triprime chain of length j is a sequence of triprimes a(1) < a(2) < ... < a(j) such that a(i+1) = 2*a(i) + 1 for i = 1, ..., j-1. The first of these are: Length 3: 332, 665, 1331 = 11^3; 387, 775, 1551 = 3 * 11 * 47.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

OEIS Wiki, Triprimes

Formula

{a(n)} = a(n) is an element of A014612 and 2*a(n)+1 is an element of A014612.

Example

n      k = a(n)           2k + 1
=  ================  ================
1   52 = 2^2 * 13    105 = 3 * 5 * 7
2   76 = 2^2 * 19    153 = 3^2 * 17
3  130 = 2 * 5 * 13  261 = 3^2 * 29
4  171 = 3^2 * 19    343 = 7^3
5  172 = 2^2 * 43    345 = 3 * 5 * 23
6  212 = 2^2 * 53    425 = 5^2 * 17

Mathematica

fQ[n_]:=PrimeOmega[n] == 3 == PrimeOmega[2 n + 1]; Select[Range@1100, fQ] (* Vincenzo Librandi, Aug 19 2018 *)

Prog

(PARI) is(n)=bigomega(n)==3 && bigomega(2*n+1)==3 \\ Charles R Greathouse IV, Feb 01 2017
(Magma) Is3primes:=func<i|&+[d[2]: d in Factorization(i)] eq 3>; [n: n in [2..1200] | Is3primes(n) and Is3primes(2*n+1)]; // Vincenzo Librandi, Aug 19 2018

Crossrefs

Cf. A005384, A014612, A111153, A111168, A111170, A111171, A111176.

Sequence in context: A043991 A326235 A118148 * A090793 A090791 A234099

Adjacent sequences: A111170 A111171 A111172 * A111174 A111175 A111176

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 21 2005

Extensions

Extended by Ray Chandler, Oct 22 2005

Edited by Jon E. Schoenfield, Aug 18 2018

Status

approved