A387616 Numbers k that are less than distance j from j! for some positive integer j.

1, 2, 3, 4, 5, 6, 7, 8, 21, 22, 23, 24, 25, 26, 27, 116, 117, 118, 119, 120, 121, 122, 123, 124, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 5034, 5035, 5036, 5037, 5038, 5039, 5040, 5041, 5042, 5043, 5044, 5045, 5046, 40313, 40314

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Example

Seen as an irregular triangle:
  1, 2, 3;         (between 2!-1 and 2!+1)
  4, 5, 6, 7, 8;   (between 3!-2 and 3!+2)
  21, 22, 23, 24, 25, 26, 27, ...;
  116, 117, 118, 119, 120, 121, 122, 123, 124, ....

Mathematica

a[n_] := Module[{m = Floor[Sqrt[n]]}, (m+1)! + n - m^2 - m]; Array[a, 50] (* Amiram Eldar, Sep 04 2025 *)

Crossrefs

Cf. A000142.

Sequence in context: A366947 A366838 A236836 * A371260 A215888 A240963

Adjacent sequences: A387613 A387614 A387615 * A387617 A387618 A387619

Keyword

nonn,easy

Author

Dwight Boddorf, Sep 03 2025

Status

approved