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A321870
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Fermat pseudoprimes to base 2 that are decagonal.
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4
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1105, 1387, 2047, 3277, 6601, 13747, 16705, 19951, 31417, 74665, 83665, 88357, 90751, 275887, 390937, 514447, 604117, 642001, 741751, 748657, 769567, 916327, 1092547, 1293337, 1302451, 1433407, 1520905, 1530787, 1809697, 1907851, 2008597, 2205967, 2387797
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OFFSET
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1,1
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COMMENTS
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Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.
The corresponding indices of the decagonal numbers are 17, 19, 23, 29, 41, 59, 65, 71, 89, 137, 145, 149, 151, 263, 313, 359, 389, 401, 431, 433, 439, 479, 523, 569, 571, 599, 617, 619, 673, 691, 709, 743, 773, 829, 863, 883, 911, 919, 941, ...
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LINKS
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MATHEMATICA
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dec[n_] := n(4n-3); Select[dec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
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PROG
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(PARI) isok(n) = (n>1) && ispolygonal(n, 10) && !isprime(n) && (Mod(2, n)^n==2); \\ Daniel Suteu, Nov 29 2018
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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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