[seqfan] Stirling-2 Numbers and dropping times of the Collatz Conjecture

peter.luschny peter.luschny at googlemail.com
Sun Jun 27 23:38:32 CEST 2010

Hi all!

I am contemplating whether the following strange connection
between the Stirling numbers of the second kind S(n,m) and
the Collatz conjecture holds. Let me state it as a conjecture:

| If the value of m maximizing m!S(n,m) equals
| M := floor(1 + (n+1)/log(4)) then M is a
| "dropping time" of the Collatz (3x+1) iteration.

See A019538 for m!S(n,m).
See A002869 for max in the n-th row of the above.
See T. D. Noe's A122437 for allowable values of
the "dropping time" of the Collatz (3x+1) iteration.

The sequence of the M's such that max = M, starts

Arguments n of the above sequence
Is this, for a(n)>10, a subsequence of A048265?
a subsequence of A159843?

Cheers, Peter


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