A046808 a(n) is the least integer greater than a(n-1) such that a(n-1)*2^a(n) + 1 is prime, a(1) = 1.

1, 2, 3, 5, 7, 14, 19, 46, 48, 62, 67, 74, 81, 89, 589, 2090, 2299, 7742, 1925975, 1989191, 2008551, 4371904, 6487918

Offset: 1

Author

Chad Davis (cad16(AT)po.cwru.edu)

Keywords

• hard
• nonn
• more

Comments

Previous name was: Recursive sequence of indices of Proth primes a*2^b + 1.

Links

• Chris K. Caldwell, The Prime Pages, 3871*2^1925976+1 (7742*2^1925975+1)
• Chris K. Caldwell, The Prime Pages, 1925975*2^1989191+1
• Chris K. Caldwell, The Prime Pages, 1989191*2^2008551+1
• Chris K. Caldwell, The Prime Pages, 2008551*2^4371904+1
• Chris K. Caldwell, The Prime Pages, 68311*2^6487924+1 (4371904*2^6487918+1)
• Y. Gallot, Proth.exe: Windows Program for Finding Large Primes

Crossrefs

Cf. A046809, A080076.

Programs

Mathematica

t = {a = 1}; Do[If[PrimeQ[a*2^n + 1], AppendTo[t, a = n]], {n, 2, 2300}]; t (* Jayanta Basu, Jun 29 2013 *)

PARI

a=1; until(, print1(a, ", "); for(b=a+1, +oo, if(ispseudoprime(a*2^b+1), a=b; break())))

Python

from gmpy2 import is_prime
from itertools import count, islice
def agen(): # generator of terms
    an = 1
    while True:
        yield an
        an = next(k for k in count(an+1) if is_prime(an*(1<Michael S. Branicky, Aug 12 2025

Extensions

a(19) from Kellen Shenton, May 08 2022

a(20) from Kellen Shenton, May 14 2022

a(21)-a(22) from Kellen Shenton, Feb 21 2025

New name, new offset and a(23) from Kellen Shenton, Aug 10 2025