A376355 Numbers that end in 1 when written in base of triangular numbers (cf. A000462).

1, 4, 7, 11, 14, 16, 19, 22, 25, 29, 32, 35, 37, 40, 43, 46, 49, 52, 56, 59, 62, 67, 70, 73, 77, 79, 82, 85, 89, 92, 95, 98, 102, 106, 109, 112, 116, 119, 121, 124, 127, 131, 134, 137, 140, 143, 147, 150, 152, 154, 157, 160, 164, 167, 169, 172, 175, 178, 182

Offset

1,2

Comments

Every positive integer is in exactly one of the following sequences: A376355, this sequence, or A376356.

Conjecture: {a(n+1) - a(n) : n >= 1} = {2,3,4,5,6}. (See related conjectures at A376354 and A376356.)

Links

Table of n, a(n) for n=1..59.

Mathematica

a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &, Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t3 = Map[a[#, 3] &, Range[200]]; (* A000462 *)
m = Mod[t3, 10]
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376354 *)
p1 = Flatten[Position[m, 1]]  (* this sequence *)
p2 = Flatten[Position[m, 2]]  (* A376356 *)
(* Peter J. C. Moses, Sep 20 2024 *)

Crossrefs

Cf. A000462, A376354, A376356, A376357.

Sequence in context: A310722 A092403 A219051 * A310723 A102737 A310724

Adjacent sequences: A376352 A376353 A376354 * A376356 A376357 A376358

Keyword

base,nonn

Author

Clark Kimberling, Sep 22 2024

Status

approved