A020167 - OEIS

A020167

Pseudoprimes to base 39.

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

1,1

COMMENTS

Composite numbers n such that 39^(n-1) == 1 (mod n).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for sequences related to pseudoprimes

EXAMPLE

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.

MAPLE

select(n -> 39 &^ (n-1) mod n = 1 and not isprime(n), [$2..10^5]); # Robert Israel, Mar 24 2017

MATHEMATICA

max = 3000; Select[Complement[Range[max], Prime[Range[PrimePi[max]]]], PowerMod[39, # - 1, #] == 1 &] (* Alonso del Arte, Mar 12 2017 *)

CROSSREFS

Cf. A001567 (pseudoprimes to base 2).

Sequence in context: A218331 A124141 A093649 * A186439 A044225 A044606

Adjacent sequences: A020164 A020165 A020166 * A020168 A020169 A020170

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved