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

1,1

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

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 *)

Prog

(Haskell)
import Math.NumberTheory.Moduli (powerMod)
a239293 n = head [c | c <- a002808_list, powerMod n c c == n]
-- Reinhard Zumkeller, Jul 11 2014
(PARI) a(n) = forcomposite(c=n+1, , if(Mod(n, c)^c==n, return(c))) \\ Felix Fröhlich, Aug 03 2018

Crossrefs

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

Cf. A002808.

Sequence in context: A173367 A214161 A265868 * A295997 A090086 A007535

Adjacent sequences: A239290 A239291 A239292 * A239294 A239295 A239296

Keyword

nonn

Author

Robert FERREOL, Mar 14 2014

Status

approved