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A020148 Pseudoprimes to base 20. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A037305 A223467 A051873

Adjacent sequences:  A020145 A020146 A020147 * A020149 A020150 A020151

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 24 21:35 EDT 2020. Contains 337322 sequences. (Running on oeis4.)