A105233 Conjectured numbers n such that the trajectory of n as defined in A003508 is unique.

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

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