A105601 Assume the conjectured terms of A105594 are the correct beginnings of the trajectories described in A003508. a(n) is a record length of b(n) iterations to arrive at the collected trajectories. This sequence cites the b(n)'s.

0, 2, 3, 7, 8, 12, 23, 40, 53, 54, 56, 72, 82, 113, 124, 129, 213, 214, 215, 216, 220

Offset

0,2

Comments

The trajectory in A003508, etc., is defined as a(1)=n, for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).

Links

Table of n, a(n) for n=0..20.

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[ a[n - 1]]], # < a[n - 1] &]; t = Table[ a[n], {n, 1500}]; f[n_] := Module[{b, k = 1}, b[1] = n; b[m_] := b[m] = b[m - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[ b[m - 1]]], # < b[m - 1] &]; While[ Position[t, b[k]] == {} && k < 1000, k++ ]; If[ k == 1000, t = Select[ Union[ Join[t, Table[ b[i], {i, 2, k}]]], # > n &]; -1, k - 1]]; lst = {{1, 0}}; Do[d = f[n]; If[d > lst[[ -1, 2]], AppendTo[lst, {n, d}]], {n, 60000}]; Transpose[ lst][[2]]

Crossrefs

Cf. A105593, the a(n)'s are in A105600.

Sequence in context: A242655 A145489 A003307 * A199971 A033082 A084406

Adjacent sequences: A105598 A105599 A105600 * A105602 A105603 A105604

Keyword

nonn

Author

R. K. Guy and Robert G. Wilson v, Apr 15 2005

Status

approved