A239293 Smallest composite c > n such that n^c == n (mod c).

4, 341, 6, 6, 10, 10, 14, 9, 12, 15, 15, 22, 21, 15, 21, 20, 34, 25, 38, 21, 28, 33, 33, 25, 28, 27, 39, 36, 35, 49, 49, 33, 44, 35, 45, 42, 45, 39, 57, 52, 82, 66, 77, 45, 55, 69, 65, 49, 56, 51, 65, 65, 65, 55, 63, 57, 65, 66, 87, 65, 91, 63, 93, 65, 70, 78, 85

Offset: 1

Author

Robert FERREOL, Mar 14 2014

Keywords

• nonn

Comments

a(n) is the smallest weak pseudoprime to base n that is > n.

If n is even and n+1 is composite, then a(n) = n+1. [Corrected by Thomas Ordowski, Aug 03 2018]

Conjecture: a(n) = n+1 if and only if n+1 is an odd composite number. - Thomas Ordowski, Aug 03 2018

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Gérard P. Michon, Weak pseudoprimes to base a

Crossrefs

Cf. A000790 (primary pretenders), A007535 (smallest pseudoprimes to base n).

Cf. A002808.

Programs

Haskell

import Math.NumberTheory.Moduli (powerMod)
a239293 n = head [c | c <- a002808_list, powerMod n c c == n]
-- Reinhard Zumkeller, Jul 11 2014

Maple

L:=NULL: for a to 100 do for n from a+1 while isprime(n) or not(a^n - a mod n =0) do od; L:=L,n od: L;

Mathematica

Table[k = n; While[k++; PrimeQ[k] || PowerMod[n, k, k] != n]; k, {n, 100}] (* T. D. Noe, Mar 17 2014 *)

PARI

a(n) = forcomposite(c=n+1, , if(Mod(n, c)^c==n, return(c))) \\ Felix Fröhlich, Aug 03 2018