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A105233 Conjectured numbers n such that the trajectory of n as defined in A003508 is unique. 1
1, 393, 412, 668, 932, 1096, 1425, 1676, 1706, 1959, 2258, 2476, 2590, 3819, 4162, 4359, 4363, 4569, 4707, 5314, 5462, 5503, 5547, 5949, 6002, 6110, 6207, 6393, 6429, 6484, 6500, 7226, 7706, 8151, 8654, 9566, 9586, 9759, 10085, 10141, 10455, 10774 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

If n is a term of this sequence then by definition all later terms in the trajectory of n are excluded.

LINKS

Table of n, a(n) for n=1..42.

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, 1200}]; 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++ ]; t = Select[ Union[ Join[t, Table[ b[i], {i, 2, k}]]], # > n &]; If[k == 1000, -1, k - 1]]; lst = {1}; Do[ If[ f[n] == -1, AppendTo[lst, n]], {n, 12500}]; lst

CROSSREFS

Cf. A003508, A105210, A105211, A105212 and A105213.

Sequence in context: A068276 A068288 A085019 * A048129 A045194 A105210

Adjacent sequences:  A105230 A105231 A105232 * A105234 A105235 A105236

KEYWORD

nonn

AUTHOR

R. K. Guy and Robert G. Wilson v, Apr 14 2005

STATUS

approved

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Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)