A376356 Positions of numbers in A000462 that end in 2.

2, 5, 8, 12, 17, 20, 23, 26, 30, 33, 38, 41, 44, 47, 50, 53, 57, 60, 63, 68, 71, 74, 80, 83, 86, 90, 93, 96, 99, 103, 107, 110, 113, 117, 122, 125, 128, 132, 138, 141, 144, 148, 155, 158, 161, 165, 170, 173, 176, 179, 183, 188, 192, 195, 198

Offset: 1

Author

Clark Kimberling, Sep 25 2024

Keywords

• nonn
• base

Comments

Every positive integer is in exactly one of the following sequences: A376354, A376355, or this sequence.

Conjecture: {a(n+1) - a(n) : n >= 1} = {3,4,5,6,7,8,9}. (See related conjectures at A376354 and A376355.)

Crossrefs

Cf. A000462, A376354, A376355, 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]]  (* A376355 *)
p2 = Flatten[Position[m, 2]]  (* this sequence *)
(* Peter J. C. Moses, Sep 20 2024 *)