A352232 a(n) is the smallest positive integer k such that 1 + k * prime(n) is a power of two.

1, 3, 1, 93, 315, 15, 13797, 89, 9256395, 1, 1857283155, 25575, 381, 178481, 84973577874915, 4885260612740877, 18900352534538475, 1101298153654301589, 483939977, 7, 6958934353, 58261485282632731311141, 23, 2901803883615, 12550996041863657440561417875

Offset: 2

Author

Alois P. Heinz, Mar 08 2022

Keywords

• nonn

Comments

All terms are odd.

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..471

Crossrefs

Cf. A000040, A000079, A000225, A000668, A007814, A014664, A059305.

Programs

Maple

a:= n-> (p-> (2^numtheory[order](2, p)-1)/p)(ithprime(n)):
seq(a(n), n=2..28);

Python

from sympy.ntheory import n_order, prime
def A352232(n): return (2**n_order(2,p:=prime(n))-1)//p # Chai Wah Wu, Mar 09 2022

Formula

a(n) = (2^A014664(n)-1)/prime(n).

A007814(a(n)*prime(n)+1) = A014664(n).

a(n) = 1 <=> n in { A059305 } <=> prime(n) in { A000668 }.

a(n)*prime(n) + 1 in { A000079 }.

a(n)*prime(n) in { A000225 }.