A117675 Numbers k such that prime(k) + prime(k+1) + prime(k+2) is prime and also there is a j such that prime(j) + prime(j+1) + prime(j+2) = prime(k).

9, 11, 13, 20, 23, 29, 47, 64, 70, 88, 121, 126, 145, 148, 153, 174, 190, 195, 201, 213, 223, 245, 294, 298, 320, 337, 369, 381, 429, 436, 445, 462, 486, 495, 504, 536, 548, 584, 596, 608, 639, 677, 747, 819, 827, 831, 868, 877, 887, 902, 905, 970

Offset: 1

Author

Roger L. Bagula, Apr 12 2006

Keywords

• nonn

Crossrefs

Cf. A109756, A072225.

Programs

PARI

isok2(k)={my(q=prime(k), p=q\3); while(p>2, p=precprime(p-1); my(p2=nextprime(p+1), t=p+p2+nextprime(p2+1)); if(t<=q, return(t==q))); 0}
isok(k)={my(p1=prime(k), p2=nextprime(p1+1), p3=nextprime(p2+1)); isprime(p1+p2+p3) && isok2(k)}
select(isok, [1..1000]) \\ Andrew Howroyd, Jul 23 2024

Extensions

Edited and more terms from Andrew Howroyd, Jul 23 2024