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A350084 a(n) = ord(2,A006935(n)/2), where ord(k,m) is the multiplicative order of k modulo m.

%I A350084 #14 Jul 21 2024 03:47:10
%S A350084 1,261,165,275,13425,1485,1305,32085,825,3465,2093,3135,495,495,261,
%T A350084 847,9405,552189,198561,261,579261,2475,6237,166725,111111,3393,3565,
%U A350084 25245,18585,4437,891891,309455,37125,4833,2301585,14355,11781,3315,915,84975,35259
%N A350084 a(n) = ord(2,A006935(n)/2), where ord(k,m) is the multiplicative order of k modulo m.
%C A350084 List of ord(2,k) where k ranges over the odd numbers such that 2^(2*k-1) == 1 (mod k).
%H A350084 Amiram Eldar, <a href="/A350084/b350084.txt">Table of n, a(n) for n = 1..1319</a>
%F A350084 a(n) = ord(2,A347906(n)) = (A006935(n) - 1) / A350083(n).
%e A350084 A006935(2) = 161038, so a(2) = ord(2,161038/2) = 261.
%e A350084 A006935(3) = 215326, so a(3) = ord(2,215326/2) = 165.
%o A350084 (PARI) list(lim) = my(v=[],d); forstep(k=1, lim, 2, if((2*k-1)%(d=znorder(Mod(2,k)))==0, v=concat(v,d))); v \\ gives a(n) for A347906(n) <= lim
%Y A350084 Cf. A006935, A347906, A350083, A306413, A306414.
%K A350084 nonn
%O A350084 1,2
%A A350084 _Jianing Song_, Dec 12 2021