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A173927
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Smallest integer k such that the number of iterations of Carmichael lambda function (A002322) needed to reach 1 starting at k (k is counted) is n.
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4
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1, 2, 3, 5, 11, 23, 47, 283, 719, 1439, 2879, 34549, 138197, 531441, 1594323, 4782969, 14348907, 43046721, 86093443, 258280327, 688747547
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OFFSET
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1,2
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COMMENTS
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Smallest number k such that the trajectory of k under iteration of Carmichael lambda function contains exactly n distinct numbers (including k and the fixed point).
The first 13 terms are 1 or a prime. The next five terms are powers of 3. Then another prime. What explains this behavior? - T. D. Noe, Mar 23 2012
If a(n) (n > 1) is either a prime or a power of 3, then a(n) is also the smallest integer k such that the number of iterations of Euler's totient function (A000010) needed to reach 1 starting at k (k is counted) is n. - Jianing Song, Jul 10 2019
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LINKS
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EXAMPLE
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for n=5, a(5)=11 gives a chain of length 5 because the trajectory is 11 -> 10 -> 4 -> 2 -> 1.
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MATHEMATICA
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f[n_] := Length@ NestWhileList[ CarmichaelLambda, n, Unequal, 2] - 1; t = Table[0, {30}]; k = 1; While[k < 2100000001, a = f@ k; If[ t[[a]] == 0, t[[a]] = k; Print[a, " = ", k]]; k++] (* slightly modified by Robert G. Wilson v, Sep 01 2014 *)
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PROG
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(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a173927 = (+ 1) . fromJust . (`elemIndex` map (+ 1) a185816_list)
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CROSSREFS
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Cf. A185816 (number of iterations of Carmichael lambda function needed to reach 1), A003434 (number of iterations of Euler's totient function needed to reach 1).
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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