A050200 Let p = prime(n). Then a(n) = p + (next prime >= p+1) + (next prime >= p+3).

10, 15, 23, 29, 41, 47, 59, 65, 81, 97, 105, 119, 131, 137, 153, 171, 187, 195, 209, 223, 231, 245, 261, 283, 299, 311, 317, 329, 335, 367, 389, 405, 425, 437, 457, 465, 483, 497, 513, 531, 551, 563, 581, 587, 607, 621, 657, 677, 689, 695, 711, 731, 743, 765

Offset: 0

Author

Cino Hilliard, May 08 2003

Keywords

• easy
• nonn

Comments

The occurrence of multiples of 3 in the sequence appears to converge to about 0.44.

Crossrefs

Cf. A034962.

Programs

Mathematica

nextprim[n_] := Block[{k = n}, While[ ! PrimeQ[k], k++ ]; k]; f[n_] := (x = Prime[n]; nextprim[x] + nextprim[x + 1] + nextprim[x + 3]); Table[ f[n], {n, 54}] (* Robert G. Wilson v, Feb 12 2005 *)
np[n_]:=Module[{pr=Prime[n]},pr+NextPrime[pr+1]+NextPrime[pr+3]]; Join[ {10}, Array[ np,60,2]] (* Harvey P. Dale, Mar 04 2015 *)

PARI

sumprime3(n) = { c1=0; c2=0; forprime(x=2,n, s = nextprime(x)+nextprime(x+1)+nextprime(x+3); c1++; if(s%3==0,c2++); print1(s" "); ); print(); print(c2/c1+.0) }

Extensions

Definition corrected by Zak Seidov, Robert G. Wilson v and Ralf Stephan, Feb 10 2005