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A020167
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Pseudoprimes to base 39.
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1
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38, 95, 133, 341, 1561, 1834, 1891, 2047, 2101, 2465, 3053, 3439, 3805, 4141, 4237, 4411, 5662, 5921, 6533, 6601, 6697, 8149, 8321, 8911, 10381, 10585, 12403, 12431, 13889, 13981, 15841, 16297, 16441, 16589, 17081, 20567, 22681, 23521, 26885, 28153
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OFFSET
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1,1
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COMMENTS
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Composite numbers n such that 39^(n-1) == 1 (mod n).
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LINKS
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EXAMPLE
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Since 39^n = 1 mod 38 as long as n is a nonzero integer, 38 is in the sequence trivially.
Obviously 39 = 39 mod 95. But 39^2 = 1521 = 16 * 95 + 1, which means that 39^n = 1 mod 95 whenever n is even, and since 95 - 1 is even, 95 is in the sequence.
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MAPLE
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select(n -> 39 &^ (n-1) mod n = 1 and not isprime(n), [$2..10^5]); # Robert Israel, Mar 24 2017
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MATHEMATICA
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max = 3000; Select[Complement[Range[max], Prime[Range[PrimePi[max]]]], PowerMod[39, # - 1, #] == 1 &] (* Alonso del Arte, Mar 12 2017 *)
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CROSSREFS
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Cf. A001567 (pseudoprimes to base 2).
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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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