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 A293623 Fermat pseudoprimes to base 2 that are pentagonal. 5
 7957, 241001, 1419607, 1830985, 1993537, 2134277, 2163001, 2491637, 2977217, 4864501, 5351537, 6952037, 10084177, 11367137, 11433301, 14609401, 21306157, 22591301, 26470501, 26977001, 29581501, 35851037, 44731051, 46517857, 53154337, 55318957, 55610837 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Rotkiewicz proved that this sequence is infinite. Intersection of A001567 and A000326. The corresponding indices of the pentagonal numbers are 73, 401, 973, 1105, 1153, 1193, 1201, 1289, 1409, 1801, 1889, 2153, 2593, 2753, 2761, ... REFERENCES Andrzej Rotkiewicz, Sur les nombres pseudopremiers pentagonaux, Bull. Soc. Roy. Sci. Liège, Vol. 33 (1964), pp. 261-263. LINKS EXAMPLE 7957 = (3*73^2 - 73)/2 is in the sequence since it is pentagonal, composite, and 2^7956 == 1 (mod 7957). MATHEMATICA p[n_]:=(3n^2-n)/2; Select[p[Range[3, 10^4]], PowerMod[2, (# - 1), #]==1 &] CROSSREFS Cf. A000326, A001567. Sequence in context: A260959 A316906 A316907 * A316908 A254138 A157660 Adjacent sequences:  A293620 A293621 A293622 * A293624 A293625 A293626 KEYWORD nonn AUTHOR Amiram Eldar, Oct 13 2017 STATUS approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)