A376357 Positions of numbers in A007961 that end in 0.

4, 8, 9, 13, 16, 20, 24, 25, 29, 33, 34, 36, 40, 44, 45, 49, 53, 57, 58, 62, 64, 68, 72, 73, 77, 80, 81, 85, 89, 90, 94, 97, 100, 104, 108, 109, 113, 116, 120, 121, 125, 129, 130, 134, 137, 141, 144, 148, 152, 153, 157, 160, 164, 168, 169, 173, 177, 178, 182

Offset: 1

Author

Clark Kimberling, Sep 25 2024

Keywords

• nonn
• base

Comments

Every positive integer is in exactly one of these sequences: this sequence, A376358, A376359, or A376360.

Conjecture: {a(n+1) - a(n) : n >= 1} = {1,2,3,4}. (See related conjectures at A376358-A376360.)

Crossrefs

Cf. A007961, A376354, A376358, A376359, A376360.

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]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* this sequence *)
p1 = Flatten[Position[m, 1]]  (* A376358 *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* A376360 *)
(* Peter J. C. Moses, Sep 20 2024 *)