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%I #10 Jan 06 2022 15:27:23
%S 341,1105,1729,29341,162401,252601,1152271,2508013,3828001,6733693,
%T 17098369,17236801,29111881,82929001,172947529,216821881,228842209,
%U 366652201,413138881,2301745249,2438403661,5255104513,5781222721,8251854001,12173703001,13946829751,15906120889,23224518901
%N Records in A083876.
%t f[1] = 341; f[2] = 1105; f[3] = 1729; f[n_] := f[n] = Block[{k = f[n -1], lp = Prime@ Range[2, n -1], p = Prime@ n}, While[ PrimeQ@ k || PowerMod[2, k -1, k] != 1 || PowerMod[p, k -1, k] != 1 || Union[ PowerMod[lp, k -1, k]] != {1}, k += 2]; k]; Union[ Table[ f@n, {n, 1012}]]
%Y Cf. A083876, A271221, A300629.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Oct 08 2021