A333743 - OEIS

A333743

Odd numbers k such that the multiplicative orders of 2 modulo k and modulo k+2 are equal.

%I #8 Apr 04 2020 04:40:53

%S 109,157,307,427,499,811,1015,1183,1459,2013,2251,2715,3181,3259,3439,

%T 3541,3889,3963,4303,4339,4553,4909,5197,6421,6661,6997,8389,8707,

%U 8779,9067,9109,9663,10531,10597,11731,12243,12259,13009,13789,14347,14437,14583,16143

%N Odd numbers k such that the multiplicative orders of 2 modulo k and modulo k+2 are equal.

%H Amiram Eldar, <a href="/A333743/b333743.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativeOrder.html">Multiplicative Order</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiplicative_order">Multiplicative order</a>.

%e 109 is a term since the multiplicative orders of 2 modulo 109 and modulo 111 are both equal to 36.

%t Select[Range[1, 10^4, 2], MultiplicativeOrder[2, #] == MultiplicativeOrder[2, # + 2] &]

%Y Cf. A002326, A333741, A333744.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 03 2020