A269345 Smaller of two consecutive odd numbers that are composites.

25, 33, 49, 55, 63, 75, 85, 91, 93, 115, 117, 119, 121, 123, 133, 141, 143, 145, 153, 159, 169, 175, 183, 185, 187, 201, 203, 205, 207, 213, 215, 217, 219, 235, 243, 245, 247, 253, 259, 265, 273, 285, 287, 289, 295, 297, 299, 301, 303, 319, 321, 323, 325, 327, 333

Offset

1,1

Comments

Analogous to A001359 for odd composite numbers (A071904).

Consists of numbers that cannot be the difference of two primes: an odd number m can be the difference of two primes only if m+2 is prime, which cannot be the case for any a(n) as a(n)+2 is composite.

Some terms form subsequences of perfect powers, e.g., A106564 (for squares) and A269346 (for cubes).

Any composite of the form 6k+1 (A016921) is a term: (6k+1)+2 = 3(2k+1) is both odd and composite as a product of two odd numbers, thus 6k+1, being odd, is a term if it is composite.

Links

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, Twin Composites

Formula

a(n) = A061673(n) - 1. - M. F. Hasler, Nov 18 2018

Example

25 belongs to this sequence because 27=25+2 is the next odd composite.

Mathematica

Select[Range[450], OddQ[#]&& !PrimeQ[#]&&!PrimeQ[#+2]&]

Prog

(PARI) for(n=1, 450, n%2==1&&!isprime(n)&&!isprime(n+2)&&print1(n, ", "))
(Magma) [n: n in [1..350]| not IsPrime(n) and not IsPrime(n+2) and n mod 2 eq 1]; // Vincenzo Librandi, Feb 28 2016

Crossrefs

Cf. A071904 (odd composites), A001359 (similar sequence for primes).

Cf. A106564, A269346.

Cf. A061673.

Sequence in context: A209333 A131610 A211466 * A134099 A129074 A188443

Adjacent sequences: A269342 A269343 A269344 * A269346 A269347 A269348

Keyword

nonn

Author

Waldemar Puszkarz, Feb 24 2016

Extensions

Name edited by Michel Marcus, Jul 27 2023

Status

approved