A330704 a(n) is the least number k for which A330437(k) = n.

1, 4, 12, 27, 26, 182, 183, 319, 280, 842, 1045, 1718, 1989, 1985, 1983, 1922, 5673, 8546, 11760, 13371, 15606, 16659, 15827, 15732, 15833, 15210, 15416, 15707, 15334, 15251, 15006, 14812, 14674, 14787, 14786, 55911, 137068, 283221, 283091, 301659, 301655, 292032, 294932, 256000

Offset

1,2

Comments

The graph of the sequence looks like a staircase: the consecutive terms differ very little, then rise significantly, then again differ very little and so on. Could someone explain this behavior?

Links

Table of n, a(n) for n=1..44.

Example

As n = 26 is the least number with the trajectory of length 5, (26, 27, 35, 39, 41), a(5) = 26.

Mathematica

Clear[f, it, order, seq]; f[n_]:=f[n]=n-1+n/FactorInteger[n][[-1]][[1]]; it[k_, n_]:=it[k, n]=f[it[k, n-1]]; it[k_, 1]=k; order[n_]:=order[n]=SelectFirst[Range[1, 100], it[n, #]==it[n, #+1]&]; seq[n_]:=seq[n]=SelectFirst[Range[350000], order[#]==n&]; seq/@Range[61]

Crossrefs

Cf. A330437.

Sequence in context: A264100 A316540 A066185 * A239940 A320923 A008107

Adjacent sequences: A330701 A330702 A330703 * A330705 A330706 A330707

Keyword

nonn,look

Author

Elijah Beregovsky, Feb 16 2020

Status

approved