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

Author

Amiram Eldar, Oct 12 2017

Keywords

• nonn

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

Examples

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

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.

Crossrefs

Cf. A002997, A090086.

Programs

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 *)