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Positive integers m such that A126289^k(m) = m for some positive integer k.
4

%I #9 Nov 01 2020 01:36:44

%S 1,6,10,15,20,21,35,38,42,45,52,58,63,66,68,74,76,77,78,84,85,88,92,

%T 99,110,116,117,124,130,133,143,146,153,164,171,187,189,198,208,224,

%U 228,232,238,246,247,255,261,266,268,272,273,279,282,284,285,304,312

%N Positive integers m such that A126289^k(m) = m for some positive integer k.

%C A126289^k(m) means apply A126289 to m k times.

%C Equivalently, the numbers that belong to a cycle under the map x -> A126289(x).

%C There are no primes in this sequence.

%H Ely Golden, <a href="/A337612/b337612.txt">Table of n, a(n) for n = 1..10000</a>

%H Ely Golden, <a href="/A337612/a337612.py.txt">Python program for (naïvely) generating terms of this sequence</a>

%F For any term m, gcd {m, A126289(m), A126289(A126289(m)), ...} = A052126(m).

%e 6 is a term since A126289(A126289(6)) = A126289(10) = 6.

%Y Cf. A052126, A126289, A337609, A337610, A337611.

%K nonn

%O 1,2

%A _Ely Golden_, Oct 06 2020