A159260 -id:A159260 - cp's OEIS frontend

A159261 Primes of the form 1 + sum_{i=1..n} 2^prime[i] for some n.

5, 13, 173, 2111, 665773, 3142394278117397493736691789093238367784438314557856426157

Offset: 1

T. D. Noe, Apr 07 2009

nonn

Primes whose binary representation has the 0 and prime bits set up to prime(n). The values of n are in A159260.

s=1; Reap[Do[s=s+2^Prime[n]; If[PrimeQ[s], Sow[s]], {n,50}]][[2,1]]

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

Original entry on oeis.org

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

Alex Ratushnyak, Sep 30 2016

nonn

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

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

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

lista(nn) = for(n=1, nn, if(isprime(1+sum(i=1, n, prime(i)^2)), print1(n, ", "))); \\ Altug Alkan, Oct 01 2016

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(n, end=', ')

cp's OEIS Frontend

A159261 Primes of the form 1 + sum_{i=1..n} 2^prime[i] for some n.

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

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