

A111170


Semiprimes S such that 3*S + 1 is also a semiprime.


5



15, 35, 38, 39, 55, 62, 82, 86, 87, 91, 106, 111, 115, 118, 119, 134, 142, 155, 159, 178, 187, 194, 218, 226, 235, 254, 259, 267, 278, 287, 295, 298, 299, 314, 319, 326, 327, 334, 335, 339, 371, 382, 386, 391, 395, 398, 411, 422, 427, 446, 451, 454, 502, 515
(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 first kind and Tomaszewski chains of the first 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, ..., k1. Length 3: 111, 334, 1003; 142, 427, 1282. Length 4: 35, 106, 319, 958; 86, 259, 778, 2335; 187, 562, 1687, 5062.


LINKS

Table of n, a(n) for n=1..54.


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 15 = 3 * 5 46 = 2 * 23
2 35 = 5 * 7 106 = 2 * 53
3 38 = 2 * 19 115 = 5 * 23
4 39 = 3 * 13 118 = 2 * 59
5 55 = 5 * 11 166 = 2 * 83
6 62 = 2 * 31 187 = 11 * 17


CROSSREFS

Cf. A001358, A111153, A111168, A111171, A111173, A111176.
Sequence in context: A205148 A253055 A338063 * A134335 A257591 A284406
Adjacent sequences: A111167 A111168 A111169 * A111171 A111172 A111173


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Oct 21 2005


EXTENSIONS

Extended by Ray Chandler, Oct 22 2005


STATUS

approved



