A105600 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 a(n)'s.

1, 5, 9, 16, 25, 43, 91, 105, 427, 463, 484, 4085, 4306, 4413, 5583, 6273, 10172, 18105, 24946, 31686, 31886

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][[1]]

Crossrefs

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

Sequence in context: A315111 A165594 A023497 * A233184 A356675 A072174

Adjacent sequences: A105597 A105598 A105599 * A105601 A105602 A105603

Keyword

nonn

Author

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

Status

approved