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A337119 Primes p such that b^(p-1) == 1 (mod p-1) for all b coprime to p-1. 0
2, 3, 5, 7, 13, 17, 19, 37, 41, 43, 61, 73, 97, 101, 109, 127, 157, 163, 181, 193, 241, 257, 313, 337, 379, 401, 421, 433, 487, 541, 577, 601, 641, 661, 673, 757, 769, 881, 883, 937, 1009, 1093, 1153, 1201, 1249, 1297, 1321, 1361, 1459, 1601, 1621, 1801, 1861, 1873, 2017, 2029, 2053, 2161, 2269, 2341, 2437, 2521, 2593 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently: primes p to p-1 a Novák-Carmichael number A124240.

These p are such that for all x in [0,p), and all b coprime to p-1, x^(b^(p-1)) == x (mod p), this follows from the FLT.

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

7 is in the sequence because it is prime, 1 and 5 are the integers (mod 6) coprime to 6; 1^6 mod 6 = 1; and 5^6 mod 6 = 1.

11 is not in the sequence because 3 is coprime to 10; and 3^10 mod 10 = 9 <> 1.

MATHEMATICA

a={}; For[p=2, p<2600, p=NextPrime[p], b=p-1; While[--b>0&&(GCD[b, p-1]!=1||PowerMod[b, p-1, p-1]==1)]; If[b==0, AppendTo[a, p]]]; a

CROSSREFS

Cf. A124240.

Sequence in context: A152961 A109461 A138539 * A090422 A005109 A247980

Adjacent sequences:  A337116 A337117 A337118 * A337120 A337121 A337122

KEYWORD

nonn

AUTHOR

Francois R. Grieu, Aug 17 2020

STATUS

approved

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Last modified September 25 05:14 EDT 2021. Contains 347652 sequences. (Running on oeis4.)