A376354 - OEIS

A376354

Numbers that end in 0 when written in base of triangular numbers (cf. A000462).

3, 6, 9, 10, 13, 15, 18, 21, 24, 27, 28, 31, 34, 36, 39, 42, 45, 48, 51, 54, 55, 58, 61, 64, 65, 66, 69, 72, 75, 76, 78, 81, 84, 87, 88, 91, 94, 97, 100, 101, 104, 105, 108, 111, 114, 115, 118, 120, 123, 126, 129, 130, 133, 135, 136, 139, 142, 145, 146, 149

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OFFSET

1,1

COMMENTS

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

Conjecture: {a(n+1) - a(n) : n >= 1} = {1, 2, 3}. (See related conjectures at A376355 and A376356.)

LINKS

Table of n, a(n) for n=1..60.

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]] (* this sequence *)

p1 = Flatten[Position[m, 1]] (* A376355 *)

p2 = Flatten[Position[m, 2]] (* A376356 *)

(* Peter J. C. Moses, Sep 20 2024 *)

CROSSREFS

Cf. A000462, A376355, A376356, A376357.

Sequence in context: A247575 A338626 A289130 * A188299 A187577 A348237

Adjacent sequences: A376351 A376352 A376353 * A376355 A376356 A376357

KEYWORD

nonn,base

AUTHOR

Clark Kimberling, Sep 22 2024

STATUS

approved