A105593 Number of steps for n to join the main line of A003508.

0, 0, 0, 0, 2, 1, 0, 0, 3, 1, 0, 0, 2, 1, 1, 7, 1, 0, 6, 5, 7, 2, 1, 0, 8, 1, 8, 4, 1, 0, 7, 6, 5, 4, 5, 1, 4, 3, 5, 5, 0, 0, 12, 11, 4, 1, 5, 4, 11, 11, 1, 10, 4, 3, 0, 4, 10, 10, 3, 2, 10, 9, 2, 11, 2, 3, 10, 9, 9, 2, 1, 0, 2, 1, 2, 1, 9, 0, 10, 9, 2, 2, 2, 1, 1, 5, 7, 8, 10, 9, 23, 4, 7, 4, 7, 8, 0, 0, 1

Offset: 1

Author

R. K. Guy and Robert G. Wilson v, Apr 13 2005

Keywords

• nonn

Comments

a(n)=0 if n is a member of A003508. First term whose value is in question is 393.

Examples

			a(5)=2 because 5=>6=>12 and 12 is the eighth term of A003508.
		

Crossrefs

Cf. A003508.

Programs

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] &]; Table[a[n], {n, 100}]; f[n_] := Module[{b, k = 1, t = Table[a[i], {i, 100}]}, 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++ ]; k - 1]; Table[ f[n], {n, 105}]