A113878 a(1)=0; a(n+1) is the least number > a(n) such that Sum_{k=1..n+1} 2^a(k) is not composite.

0, 1, 2, 4, 7, 16, 53, 66, 207, 1752, 5041, 6310

Offset: 1

Author

Artur Jasinski, Jan 27 2006

Keywords

• nonn
• more

Comments

Base-2 logarithms of A073924.

a(13) > 50000. - Don Reble

Crossrefs

Cf. A073924, A080355, A080567, A113824.

Programs

Mathematica

a[1] = 0; a[n_] := a[n] = Block[{k = a[n - 1] + 1, s = Plus @@ (2^Array[a, n - 1])}, While[ !PrimeQ[s + 2^k], k++ ]; k]; Array[a, 12] (* Robert G. Wilson v *)

Python

from sympy import isprime
def afind(limit):
    print("0, 1", end=", ")
    s, pow2 = 2**0 + 2**1, 2**2
    for m in range(2, limit+1):
        if isprime(s+pow2): print(m, end=", "); s += pow2
        pow2 *= 2
afind(2000) # Michael S. Branicky, Jul 11 2021

Extensions

Edited by Don Reble, Feb 17 2006