A133659 Primes that are the sum of three consecutive primes as well as the sum of three consecutive composite numbers.

23, 31, 41, 59, 71, 109, 131, 199, 211, 251, 269, 311, 487, 503, 701, 829, 941, 1049, 1061, 1151, 1229, 1381, 1511, 1931, 2129, 2179, 2251, 2269, 2393, 2579, 2971, 3041, 3271, 3329, 3581, 3851, 3889, 3911, 4289, 4451, 4481, 4679, 4987, 4999

Offset: 1

Author

Randy L. Ekl, Dec 28 2007

Keywords

• easy
• nonn

Examples

			a(3) = 41 because 41 = 11+13+17 and 41 = 12+14+15.
		

Links

• R. J. Mathar, Table of n, a(n) for n=1..287

Crossrefs

Cf. A034962, A060328.

Programs

Mathematica

a = {}; For[n = 2, n < 10000, n++, If[ ! PrimeQ[n], AppendTo[a, n + Select[Range[n + 1, n + 10], ! PrimeQ[ # ] &][[1]] + Select[Range[n + 1, n + 10], ! PrimeQ[ # ] &][[2]]]]]; b = Table[Prime[i] + Prime[i + 1] + Prime[i + 2], {i, 1, 10000}]; Select[Intersection[a, b], PrimeQ[ # ] &] (* Stefan Steinerberger, Dec 30 2007 *)

Formula

Equals A034962 INTERSECT A060328. - R. J. Mathar, Jan 11 2008

Extensions

More terms from Stefan Steinerberger, Dec 30 2007