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A343269 a(n) is the smallest integer whose orbit length is n under iteration of the map r -> A061602(r). 0
1, 0, 169, 78, 69, 26, 24, 4, 22, 5, 122, 25, 14, 127, 6, 3, 12, 33, 136, 256, 57, 247, 148, 38, 1478, 368, 79, 1458, 48, 44, 29, 7, 13, 34, 9, 8, 23, 234, 37, 337, 58, 46, 139, 138, 369, 239, 267, 36, 334, 289, 3555, 49, 144, 45, 229, 2569, 22888, 136789, 334479, 1479, 1233466 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A303935 provides the orbit's lengths, i.e., the number of needed steps, starting from a given number, to reach a value that already exists in trajectory.
This sequence is infinite. Actually, given a number x whose orbit's length is k, one can always build a number y whose orbit's length is (k+1).
For instance, just consider either the number 10^(x-1), or Rx (the repunit of length x), or any other x-digit binary string, all of them leading to the number x after application of the mapping function: A061602(y) = x.
Indeed, none of them will correspond to the smallest integer m such that A303935(m) = k + 1.
In fact, it becomes computationally hard to determine further terms since, as in the Collatz mapping function and other similar problems, there is no predictable way to define the exact complete path without calculating all intermediary orbit's components until one reaches a previously calculated or encountered number.
a(59) = 334479, a(60) = 1479, a(61) = 1233466, next terms = ?
LINKS
EXAMPLE
a(6) = 26 because A303935(26) = 6, and 26 is the smallest nonnegative integer m such that A303935(m) = 6.
CROSSREFS
Cf. A303935 (orbit's length), A061602 (sum of factorials of digits), A014080 (factorions).
Sequence in context: A003797 A297048 A003929 * A240069 A184035 A044869
KEYWORD
nonn,base
AUTHOR
Lamine Ngom, Apr 10 2021
STATUS
approved

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Last modified February 22 05:23 EST 2024. Contains 370239 sequences. (Running on oeis4.)