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

Author

Clark Kimberling, Sep 22 2024

Keywords

• base
• nonn

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.)

Crossrefs

Cf. A000462, A376354, A376356, A376357.

Programs

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 *)