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%I #8 May 22 2013 15:11:43
%S 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,
%T 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,
%U 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
%N Number of steps for n to join the main line of A003508.
%C a(n)=0 if n is a member of A003508. First term whose value is in question is 393.
%e a(5)=2 because 5=>6=>12 and 12 is the eighth term of A003508.
%t 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}]
%Y Cf. A003508.
%K nonn
%O 1,5
%A _R. K. Guy_ and _Robert G. Wilson v_, Apr 13 2005
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