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A352232
a(n) is the smallest positive integer k such that 1 + k * prime(n) is a power of two.
1
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 08 2022
STATUS
approved