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A293623
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Fermat pseudoprimes to base 2 that are pentagonal.
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8
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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
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OFFSET
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1,1
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COMMENTS
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Rotkiewicz proved that this sequence is infinite.
The corresponding indices of the pentagonal numbers are 73, 401, 973, 1105, 1153, 1193, 1201, 1289, 1409, 1801, 1889, 2153, 2593, 2753, 2761, ...
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REFERENCES
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Andrzej Rotkiewicz, Sur les nombres pseudopremiers pentagonaux, Bull. Soc. Roy. Sci. Liège, Vol. 33 (1964), pp. 261-263.
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LINKS
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EXAMPLE
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7957 = (3*73^2 - 73)/2 is in the sequence since it is pentagonal, composite, and 2^7956 == 1 (mod 7957).
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MATHEMATICA
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p[n_]:=(3n^2-n)/2; Select[p[Range[3, 10^4]], PowerMod[2, (# - 1), #]==1 &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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