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Search: id:A105601
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| A105601 |
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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. |
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+0
1
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| 0, 2, 3, 7, 8, 12, 23, 40, 53, 54, 56, 72, 82, 113, 124, 129, 213, 214, 215, 216, 220
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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).
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MATHEMATICA
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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]]
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CROSSREFS
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Cf. A105593, the a(n)'s are in A105600.
Sequence in context: A032967 A111101 A003307 this_sequence A033082 A084406 A075648
Adjacent sequences: A105598 A105599 A105600 this_sequence A105602 A105603 A105604
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KEYWORD
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nonn
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca and Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 15 2005
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