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A293623
Fermat pseudoprimes to base 2 that are pentagonal.
8
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
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
Sequence in context: A260959 A316906 A316907 * A316908 A254138 A157660
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 13 2017
STATUS
approved