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A111171 Semiprimes S such that 3*S - 1 is also a semiprime. 6
9, 21, 22, 25, 26, 49, 62, 65, 69, 74, 85, 93, 121, 122, 129, 133, 141, 146, 158, 161, 166, 178, 185, 194, 205, 209, 221, 249, 253, 262, 265, 289, 298, 302, 305, 309, 346, 358, 361, 365, 381, 382, 386, 413, 446, 466, 473, 485, 489, 493, 501, 505, 514, 526, 553 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is analogous to Sophie Germain semiprimes A111153 and the chains shown are analogous to Cunningham chains of the second kind and Tomaszewski chains of the second kind. Define a 3n-1 semiprime chain of length k. This is a sequence of semiprimes s(1) < s(2) < ... < s(k) such that s(i+1) = 3*s(i) - 1 for i = 1, ..., k-1. Length 3: 9, 26, 77; 49, 146, 437; 65, 194, 581; 129, 386, 1157; 158, 473, 1418; 187, 562, 1685. Length 4: 74, 221, 662, 1985; 122, 365, 1094, 3281. Length 5: 21, 62, 185, 554, 1661.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

{a(n)} = a(n) is an element of A001358 and 3*a(n)-1 is an element of A001358.

EXAMPLE

n s(n) 3 *s -1

1 9 = 3^2 26 = 2 * 13

2 21 = 3 * 7 62 = 2 * 31

3 22 = 2 * 11 65 = 5 * 13

4 25 = 5^2 74 = 2 * 37

5 26 = 2 * 13 77 = 7 * 11

6 49 = 7^2 146 = 2 * 73

MATHEMATICA

Select[Range[600], PrimeOmega[#]==PrimeOmega[3#-1]==2&] (* Harvey P. Dale, Jun 20 2018 *)

CROSSREFS

Cf. A001358, A111153, A111168, A111170, A111173, A111176.

Sequence in context: A259250 A251219 A284131 * A317789 A333039 A266000

Adjacent sequences:  A111168 A111169 A111170 * A111172 A111173 A111174

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Oct 21 2005

EXTENSIONS

Corrected and extended by Ray Chandler, Oct 22 2005

STATUS

approved

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Last modified April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)