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A111168 Semiprimes n such that 2*n - 1 is also a semiprime. 7
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
Sequence in context: A132415 A292931 A067810 * A349865 A195331 A175426
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 April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)