A293203 Numbers k such that A090086(k), the smallest pseudoprime to base k (not necessarily exceeding k), is a Carmichael number.

700, 1040, 1150, 1848, 2590, 2660, 6710, 6862, 7000, 7716, 7852, 8060, 8528, 9275, 9875, 10103, 10640, 11830, 12010, 12688, 13340, 16520, 17350, 17570, 17960, 18130, 18340, 19203, 19272, 19420, 19820, 19978, 20410, 20442, 20480, 20612, 20720, 23016, 23463

Offset

1,1

Comments

The corresponding Carmichael numbers are 561, 561, 561, 1105, 561, 561, 1729, 561, 561, 1105, 561, 561, 561, 561, 561, 561, 561, 561, 561, ...

Andrzej Schinzel proved that this sequence is infinite. Conjecture: if A090086(n) is a Carmichael number k, then k < n. - Thomas Ordowski, Aug 08 2018

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Andrzej Rotkiewicz, Periodic sequences of pseudoprimes connected with Carmichael number and the least period of the function l_x^C, Acta Arithmetica, Vol. 91, No. 1 (1999), pp. 75-83.

Andrzej Rotkiewicz, Solved and unsolved problems on pseudoprime numbers and their generalizations, Applications of Fibonacci numbers, Springer Netherlands, 1999, pp. 293-306.

Example

700 is the sequence since A090086(700) = 561 is a Carmichael number.

Mathematica

carmichaelQ[n_] := Divisible[n - 1, CarmichaelLambda[n]] && ! PrimeQ[n];
f[n_] := Block[{k = 1}, While[GCD[n, k] > 1 || PrimeQ[k] || PowerMod[n, k - 1, k] != 1, j = k++]; k]; Select[Range[10000], carmichaelQ[f[#]] &] (* after Robert G.Wilson v at A090086 *)

Crossrefs

Cf. A002997, A090086.

Sequence in context: A133251 A243837 A116338 * A157366 A293279 A250530

Adjacent sequences: A293200 A293201 A293202 * A293204 A293205 A293206

Keyword

nonn

Author

Amiram Eldar, Oct 12 2017

Status

approved