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

2,2

Comments

All terms are odd.

Links

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

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 }.

Maple

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

Prog

(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

Crossrefs

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

Sequence in context: A370431 A331778 A241191 * A221195 A071291 A049330

Adjacent sequences: A352229 A352230 A352231 * A352233 A352234 A352235

Keyword

nonn

Author

Alois P. Heinz, Mar 08 2022

Status

approved