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

Author

Waldemar Puszkarz, Feb 24 2016

Keywords

• nonn

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.

Examples

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

Links

• Eric Weisstein's World of Mathematics, Twin Composites

Crossrefs

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

Cf. A106564, A269346.

Cf. A061673.

Programs

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

Mathematica

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

PARI

for(n=1, 450, n%2==1&&!isprime(n)&&!isprime(n+2)&&print1(n, ", "))

Formula

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

Extensions

Name edited by Michel Marcus, Jul 27 2023