A376356 -id:A376356 - cp's OEIS frontend

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

Offset: 1

Clark Kimberling, Sep 22 2024

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.)

Cf. A000462, A376355, A376356, A376357.

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 *)

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

Original entry on oeis.org

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

Clark Kimberling, Sep 22 2024

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.)

Cf. A000462, A376354, A376356, A376357.

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 *)

cp's OEIS Frontend

A376354 Numbers that end in 0 when written in base of triangular numbers (cf. A000462).

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