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%I
%S 4,7,17,20,24,27,29,40,45,48,49,53,55,57,61,62,65,67,72,76,79,82,83,
%T 85,88,91,95,100,101,106,107,109,112,119,124,136,139,142,149,151,153,
%U 158,159,164,165,167,171,178,186,189,193,197,198,202,204,209,210,215,219
%N Numbers n such that mod(3^n,2^n) is less than mod(3^(n-1),2^(n-1)).
%C Also positions where A002380(n) < A002380(n-1).
%C The first occurrence of k in the first forward difference: 48, 27, 4, 20, 40, 358, 112, 178, 222, 7, ...,.
%e 1 == 3^4 (mod 2^4) which is less than 3 == 3^3 (mod 2^3) so 4 is a member.
%t pm = 0; lst = {}; Do[pn = PowerMod[3, n, 2^n]; If[pn < pm, AppendTo[lst, n]]; pm = pn, {n, 221}]; lst
%Y Cf. A002380.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Dec 14 2006
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