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A111173 Sophie Germain triprimes: k and 2k + 1 are both the product of 3 primes, not necessarily distinct. 9
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 (list; graph; refs; listen; history; text; internal format)
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

OeisWiki, 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

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

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)