cp's OEIS Frontend

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

%I A050207 #19 May 01 2021 02:23:44
%S A050207 23,29,41,47,59,97,131,137,223,283,311,317,367,389,457,563,587,607,
%T A050207 677,743,839,857,907,929,941,947,1031,1049,1093,1283,1303,1453,1489,
%U A050207 1847,1867,1913,1931,1993,2027,2347,2381,2441,2477,2579,2617,2657
%N A050207 Primes of the form p + (smallest prime >= p+1) + (smallest prime >= p+3) where p is a prime.
%C A050207 Originally an erroneous version of A034962.
%H A050207 Charles R Greathouse IV, <a href="/A050207/b050207.txt">Table of n, a(n) for n = 1..10000</a>
%e A050207 p = 5: 23 = 5 + 7 + 11;
%e A050207 p = 7: 29 = 7 + 11 + 11;
%e A050207 p = 11: 41 = 11 + 13 + 17;
%e A050207 p = 13: 47 = 13 + 17 + 17;
%e A050207 p = 17: 59 = 17 + 19 + 23;
%e A050207 p = 19: 65 = 19 + 23 + 23 is not prime, so not in the sequence;
%e A050207 p = 23: 81 = 23 + 29 + 29 is not prime, so not in the sequence;
%e A050207 p = 29: 97 = 29 + 31 + 37.
%t A050207 Select[Table[p+NextPrime[p]+NextPrime[p+2],{p,Prime[Range[300]]}],PrimeQ] (* _Harvey P. Dale_, Dec 04 2017 *)
%o A050207 (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) }
%Y A050207 Cf. A034962.
%K A050207 nonn
%O A050207 1,1
%A A050207 _Cino Hilliard_, May 08 2003
%E A050207 Edited by _Joshua Zucker_, Jan 27 2007
%E A050207 Definition clarified by _Harvey P. Dale_, Dec 04 2017