A050207 Primes of the form p + (smallest prime >= p+1) + (smallest prime >= p+3) where p is a prime.

23, 29, 41, 47, 59, 97, 131, 137, 223, 283, 311, 317, 367, 389, 457, 563, 587, 607, 677, 743, 839, 857, 907, 929, 941, 947, 1031, 1049, 1093, 1283, 1303, 1453, 1489, 1847, 1867, 1913, 1931, 1993, 2027, 2347, 2381, 2441, 2477, 2579, 2617, 2657

Offset: 1

Author

Cino Hilliard, May 08 2003

Keywords

• nonn

Comments

Originally an erroneous version of A034962.

Examples

			p = 5: 23 = 5 + 7 + 11;
p = 7: 29 = 7 + 11 + 11;
p = 11: 41 = 11 + 13 + 17;
p = 13: 47 = 13 + 17 + 17;
p = 17: 59 = 17 + 19 + 23;
p = 19: 65 = 19 + 23 + 23 is not prime, so not in the sequence;
p = 23: 81 = 23 + 29 + 29 is not prime, so not in the sequence;
p = 29: 97 = 29 + 31 + 37.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034962.

Programs

Mathematica

Select[Table[p+NextPrime[p]+NextPrime[p+2],{p,Prime[Range[300]]}],PrimeQ] (* Harvey P. Dale, Dec 04 2017 *)

PARI

psumpr3(n) = { c1=0; c2=0; forprime(x=3, n, s = nextprime(x)+nextprime(x+1)+nextprime(x+3); c1++; if(isprime(s), c2++; print1(s" ")); ); print(); print(c2/c1+.0) }

Extensions

Edited by Joshua Zucker, Jan 27 2007

Definition clarified by Harvey P. Dale, Dec 04 2017