A259630 a(n) is the smallest integer not occurring earlier such that 2^a(1) + 2^a(2) + ... + 2^a(n) is a prime.

1, 0, 2, 4, 3, 12, 5, 14, 27, 8, 25, 30, 31, 36, 13, 18, 131, 60, 133, 458, 247, 1040, 21, 618, 283, 300, 209, 6282, 19107, 11792, 3401, 30214, 1211, 3044, 15989, 30194

Offset: 1

Author

Thomas Ordowski, Sep 24 2015

Keywords

• nonn
• more

Comments

Is this sequence infinite?

Associated primes: A059661.

Essentially the same as A059662: 1 followed by A059662. - R. J. Mathar, Oct 09 2015

a(37) > 145000. - Giovanni Resta, Jul 01 2019

Examples

			a(1) = 1 since 2^0 = 1 is not prime, but 2^1 = 2 is prime.
a(2) = 0 since 2^1 + 2^0 = 2 + 1 = 3 is prime.
a(3) = 2 since 2^1 + 2^0 + 2^2 = 2 + 1 + 4 = 7 is prime.
		

Crossrefs

Cf. A059662, A113878.

Programs

PARI

findsm(va, n) = {m = 0; ok = 0; vs = vecsort(va); sa = sum(k=1, #va, 2^va[k]); while (!ok, if (! vecsearch(vs, m), ns = sa + 2^m; if (isprime(ns), ok = 1; break);); m++;); m;}
lista(nn) = {va = []; for (n=1, nn, m = findsm(va, n); va = concat(va, m); print1(m, ", "););} \\ Michel Marcus, Sep 26 2015

Python

from sympy import isprime
A259630_list, A259630_set, k = [], set(), 0
while len(A259630_list) < 50:
    n, m = 0,1
    k += m
    while n in A259630_set or not isprime(k):
        n += 1
        k += m
        m *= 2
    A259630_list.append(n)
    A259630_set.add(n) # Chai Wah Wu, Jun 27 2019

Extensions

a(18)-a(25) from Michel Marcus, Sep 26 2015

a(26)-a(28) from Joerg Arndt (with ispseudoprime() in Pari), Sep 28 2015

a(29)-a(34) from Chai Wah Wu, Jun 27 2019

a(35)-a(36) from Giovanni Resta, Jun 30 2019