A020148 Pseudoprimes to base 20.

21, 57, 133, 231, 399, 561, 671, 861, 889, 1281, 1653, 1729, 1891, 2059, 2413, 2501, 2761, 2821, 2947, 3059, 3201, 4047, 5271, 5461, 5473, 5713, 5833, 6601, 6817, 7999, 8421, 8911, 11229, 11557, 11837, 12801, 13051, 13981, 14091, 15251, 15311, 15841

Offset

1,1

Comments

Composite numbers n such that 20^(n - 1) == 1 (mod n). - Michel Lagneau, Feb 18 2012

Links

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

Index entries for sequences related to pseudoprimes

Example

20^20 = 104857600000000000000000000 == 1 (mod 21), so 21 is in the sequence.
20^22 = 41943040000000000000000000000 == 1 (mod 23), but 23 is actually prime, so it's not in the sequence.
20^24 = 16777216000000000000000000000000 == 0 (mod 25), so 25 is not in the sequence either.

Mathematica

base = 20; pp20 = {}; n = 1; While[Length[pp20] < 100, n++; If[!PrimeQ[n] && PowerMod[base, n - 1, n] == 1, AppendTo[pp20, n]]]; pp20 (* T. D. Noe, Feb 21 2012 *)
searchMax = 10000; Complement[Select[Range[searchMax], PowerMod[20, # - 1, #] == 1 &], Prime[Range[PrimePi[searchMax]]]] (* Alonso del Arte, Feb 20 2020 *)

Crossrefs

Cf. A001567 (pseudoprimes to base 2).

Sequence in context: A044504 A118057 A327902 * A370519 A037305 A370109

Adjacent sequences: A020145 A020146 A020147 * A020149 A020150 A020151

Keyword

nonn

Author

David W. Wilson

Status

approved