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

1, 7, 23, 31, 47, 49, 71, 73, 79, 89, 103, 127, 151, 161, 167, 191, 199, 217, 223, 233, 239, 263, 271, 311, 329, 337, 343, 359, 367, 383, 431, 439, 463, 479, 487, 497, 503, 511, 529, 553, 599, 601, 607, 623, 631, 647, 713, 719, 721, 727, 743, 751

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Odd numbers k such that A007733(k) = A002326((k-1)/2) is odd.

Closed under multiplication. - Emmanuel Vantieghem, May 07 2025

Examples

			2^3 = 1 mod 7, 3 is odd, so 7 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002326, A007733, A036260, A053006.

Programs

Mathematica

Select[Range[1, 999, 2], OddQ[MultiplicativeOrder[2, #]]&] (* Jean-François Alcover, Dec 20 2017 *)

PARI

is(n)=n%2 && znorder(Mod(2,n))%2 \\ Charles R Greathouse IV, Jun 24 2015

Python

from sympy import n_order
from itertools import count, islice
def A036259_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:n_order(2,n)&1,count(max(startvalue,1)|1,2))
A036259_list = list(islice(A036259_gen(),20)) # Chai Wah Wu, Feb 07 2023