cp's OEIS Frontend

A036259 Numbers k such that the multiplicative order of 2 modulo k is odd.

%I A036259 #39 May 12 2025 00:10:19
%S A036259 1,7,23,31,47,49,71,73,79,89,103,127,151,161,167,191,199,217,223,233,
%T A036259 239,263,271,311,329,337,343,359,367,383,431,439,463,479,487,497,503,
%U A036259 511,529,553,599,601,607,623,631,647,713,719,721,727,743,751
%N A036259 Numbers k such that the multiplicative order of 2 modulo k is odd.
%C A036259 Odd numbers k such that A007733(k) = A002326((k-1)/2) is odd.
%C A036259 Closed under multiplication. - _Emmanuel Vantieghem_, May 07 2025
%H A036259 Amiram Eldar, <a href="/A036259/b036259.txt">Table of n, a(n) for n = 1..10000</a>
%e A036259 2^3 = 1 mod 7, 3 is odd, so 7 is in the sequence.
%t A036259 Select[Range[1, 999, 2], OddQ[MultiplicativeOrder[2, #]]&] (* _Jean-François Alcover_, Dec 20 2017 *)
%o A036259 (PARI) is(n)=n%2 && znorder(Mod(2,n))%2 \\ _Charles R Greathouse IV_, Jun 24 2015
%o A036259 (Python)
%o A036259 from sympy import n_order
%o A036259 from itertools import count, islice
%o A036259 def A036259_gen(startvalue=1): # generator of terms >= startvalue
%o A036259     return filter(lambda n:n_order(2,n)&1,count(max(startvalue,1)|1,2))
%o A036259 A036259_list = list(islice(A036259_gen(),20)) # _Chai Wah Wu_, Feb 07 2023
%Y A036259 Cf. A002326, A007733, A036260, A053006.
%K A036259 nonn
%O A036259 1,2
%A A036259 _David W. Wilson_