A072525 a(0) = 1; a(n+1) is smallest composite number > a(n) such that a(n) + a(n+1) is prime.

1, 4, 9, 10, 21, 22, 25, 28, 33, 34, 39, 40, 49, 52, 55, 58, 69, 70, 81, 82, 85, 88, 91, 100, 111, 112, 115, 118, 121, 130, 133, 136, 141, 142, 165, 166, 171, 176, 177, 182, 185, 188, 195, 202, 207, 212, 219, 220, 237, 242, 245, 246, 253, 256, 265, 276, 287, 290

Offset: 0

Author

Amarnath Murthy, Jul 31 2002

Keywords

• nonn

Comments

The value of a(0) is of minor importance; starting with a(0) = 2, 3, 4, 5, ... results in sequences that differ from this sequence only in a few initial terms.

22, 25, 28 are three and 49,52,55,58 are four consecutive terms in arithmetic progression. Are there k consecutive terms in arithmetic progression for every k?

Examples

			34 is the next term after 33 since 34 is composite and 33 + 34 = 67 is prime.
		

Crossrefs

Cf. A051884, A075570, A262159.

Programs

Mathematica

a=4;lst={a};Do[b=a+1;While[ !PrimeQ[a+b]&&PrimeQ[b],b++ ];AppendTo[lst,b];a=b,{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)

PARI

{print1(a=1,","); while(a<290,b=a+1; while(isprime(b)||!isprime(a+b),b++); print1(b,","); a=b)}

Extensions

Edited and extended by Klaus Brockhaus, Aug 01 2002