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

%I A352232 #19 Mar 09 2022 16:54:19
%S A352232 1,3,1,93,315,15,13797,89,9256395,1,1857283155,25575,381,178481,
%T A352232 84973577874915,4885260612740877,18900352534538475,
%U A352232 1101298153654301589,483939977,7,6958934353,58261485282632731311141,23,2901803883615,12550996041863657440561417875
%N A352232 a(n) is the smallest positive integer k such that 1 + k * prime(n) is a power of two.
%C A352232 All terms are odd.
%H A352232 Alois P. Heinz, <a href="/A352232/b352232.txt">Table of n, a(n) for n = 2..471</a>
%F A352232 a(n) = (2^A014664(n)-1)/prime(n).
%F A352232 A007814(a(n)*prime(n)+1) = A014664(n).
%F A352232 a(n) = 1 <=> n in { A059305 } <=> prime(n) in { A000668 }.
%F A352232 a(n)*prime(n) + 1 in { A000079 }.
%F A352232 a(n)*prime(n) in { A000225 }.
%p A352232 a:= n-> (p-> (2^numtheory[order](2, p)-1)/p)(ithprime(n)):
%p A352232 seq(a(n), n=2..28);
%o A352232 (Python)
%o A352232 from sympy.ntheory import n_order, prime
%o A352232 def A352232(n): return (2**n_order(2,p:=prime(n))-1)//p # _Chai Wah Wu_, Mar 09 2022
%Y A352232 Cf. A000040, A000079, A000225, A000668, A007814, A014664, A059305.
%K A352232 nonn
%O A352232 2,2
%A A352232 _Alois P. Heinz_, Mar 08 2022