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

1,5

Comments

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

Links

Table of n, a(n) for n=1..99.

Example

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

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}]

Crossrefs

Cf. A003508.

Sequence in context: A132013 A105820 A136263 * A029371 A114374 A111505

Adjacent sequences: A105590 A105591 A105592 * A105594 A105595 A105596

Keyword

nonn

Author

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

Status

approved