A053845 Primes of form prime(1) + ... + prime(k) + 1.

3, 11, 29, 59, 101, 239, 569, 1061, 1481, 1721, 4889, 5351, 6871, 22549, 23593, 25801, 29297, 35569, 38239, 41023, 71209, 77137, 87517, 94057, 105541, 120349, 122921, 125509, 128113, 133387, 138869, 141677, 156109, 159073, 165041, 183707

Offset: 1

Author

Enoch Haga, Mar 28 2000

Keywords

• easy
• nonn

Examples

			prime(1) + 1 = 2 + 1 = 3 (prime, thus a(1));
prime(1) + prime(2) + 1 = 2 + 3 + 1 = 6 (nonprime);
prime(1) + prime(2) + prime(3) + 1 = 2 + 3 + 5 + 1 = 11 (prime, thus a(2)); etc. - _Jon E. Schoenfield_, Jan 09 2015
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A013918, A089228.

Programs

Mathematica

p=1;lst={};Do[p+=Prime[n];If[PrimeQ[p],AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)

PARI

lista(nn) = {s = 1; for (n=1, nn, s += prime(n); if (isprime(s), print1(s, ", ")););} \\ Michel Marcus, Jan 10 2015

UBASIC

10 x=x+1; 20 if x<>prmdiv(x) then 10; 30 y=x; 40 r=r+y; 50 if r=prmdiv(r) then print r;:p=p+1; 60 if p<100 then 10

Formula

a(n) = A007504(A089228(n)) + 1. - Amiram Eldar, Apr 29 2024