A346216 -id:A346216 - cp's OEIS frontend

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A373056 Numbers k that divide the k-th Ulam number.

Original entry on oeis.org

1, 2, 3, 4, 16, 52, 204, 255, 4259, 4262, 4265, 4855

Offset: 1

Amiram Eldar, May 21 2024

Numbers k such that k | A002858(k).
a(13) >= 10^8, if it exists.
Based on empirical data its seems that the Ulam numbers have a positive asymptotic density and that A002858(k) ~ 13.5... * k (see A307331 and A346216). If this is true, then this sequence is finite, and it is likely that there are no more terms.

			16 is a term since A002858(16) = 48 = 3 * 16 is divisible by 16.

Index entries for Ulam numbers.

Cf. A002858, A307331, A346216.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

ulams = {1, 2}; Do[AppendTo[ulams, n = Last[ulams]; While[n++; Length[DeleteCases[ Intersection[ulams, n - ulams], n/2, 1, 1]] != 2]; n], {5000}];
Position[ulams/Range[Length[ulams]], ?IntegerQ] // Flatten (* after _Jean-François Alcover at A002858 *)

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