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 A293203 Numbers k such that A090086(k), the smallest pseudoprime to base k (not necessarily exceeding k), is a Carmichael number. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 27 12:30 EDT 2020. Contains 337380 sequences. (Running on oeis4.)