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A111168 Semiprimes n such that 2*n - 1 is also a semiprime. 6
25, 26, 33, 35, 39, 46, 58, 62, 65, 85, 93, 94, 111, 118, 119, 133, 134, 145, 146, 155, 161, 178, 183, 202, 206, 209, 214, 219, 226, 235, 237, 247, 249, 253, 259, 265, 267, 287, 291, 295, 299, 334, 335, 341, 361, 362, 377, 382, 386, 391, 393, 395, 407, 422 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Define an m-th degree Tomaszewski n-chain of the first (second) kind and length k to be a sequence of n-almost primes p(1) < p(2) < ... < p(k) such that s(i+1) = m*s(i) +(-) 1 for i = 1, ..., k-1. Notice that a 2nd degree Tomaszewski 1-chain of the first (second) kind is the familiar Cunningham chain of the first (second) kind.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

{a(n)} = a(n) is an element of A001358 and 2*a(n)-1 is an element of A001358.

EXAMPLE

n s(n) s*2-1

1 25 = 5^2 49 = 7^2

2 26 = 2 * 13 51 = 3 * 17

3 33 = 3 * 11 65 = 5 * 13

4 35 = 5 * 7 69 = 3 * 23

5 39 = 3 * 13 77 = 7 * 11

MATHEMATICA

Select[Range[500], PrimeOmega[#]==2&&PrimeOmega[2#-1]==2&] (* Harvey P. Dale, Aug 30 2015 *)

PROG

(PARI) is(n)=bigomega(n)==2 && bigomega(2*n-1)==2 \\ Charles R Greathouse IV, Jan 31 2017

CROSSREFS

Cf. A001358, A111153, A111170, A111171, A111173, A111176.

Sequence in context: A132415 A292931 A067810 * A195331 A175426 A045567

Adjacent sequences:  A111165 A111166 A111167 * A111169 A111170 A111171

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Oct 21 2005

EXTENSIONS

Extended by Ray Chandler, Oct 22 2005

STATUS

approved

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Last modified December 18 19:04 EST 2018. Contains 318243 sequences. (Running on oeis4.)