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

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..12.

Index entries for Ulam numbers.

Example

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

Mathematica

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 *)

Crossrefs

Cf. A002858, A307331, A346216.

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

Sequence in context: A283515 A333802 A229546 * A365574 A343494 A300855

Adjacent sequences: A373053 A373054 A373055 * A373057 A373058 A373059

Keyword

nonn,more

Author

Amiram Eldar, May 21 2024

Status

approved