A277123 Numbers k such that 1 + Sum_{j=1..k} prime(j)^2 is prime.

1, 11, 19, 29, 37, 73, 97, 155, 163, 175, 191, 257, 295, 313, 325, 341, 365, 389, 391, 409, 415, 461, 491, 497, 515, 599, 697, 715, 757, 761, 767, 775, 785, 793, 857, 875, 895, 899, 905, 919, 1099, 1109, 1117, 1139, 1151, 1163, 1225, 1271, 1279, 1295, 1309

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

Position[Accumulate[Prime[Range[2000]]^2]+1, _?PrimeQ]//Flatten (* Harvey P. Dale, Sep 07 2019 *)

Prog

(Python)
import sympy
sum = p = 1
for n in range(1, 3001):
  while not sympy.isprime(p):  p+=1    # find the n'th prime
  sum += p*p
  p+=1
  if sympy.isprime(sum):  print str(n)+', ',
(PARI) lista(nn) = for(n=1, nn, if(isprime(1+sum(i=1, n, prime(i)^2)), print1(n, ", "))); \\ Altug Alkan, Oct 01 2016

Crossrefs

Cf. A000040, A013916, A089228, A131694, A159260.

Sequence in context: A268271 A053032 A342961 * A034099 A034109 A155070

Adjacent sequences: A277120 A277121 A277122 * A277124 A277125 A277126

Keyword

nonn

Author

Alex Ratushnyak, Sep 30 2016

Status

approved