A376360 Positions of numbers in A007961 that end in 3.

3, 7, 12, 19, 23, 28, 32, 39, 43, 48, 52, 56, 61, 67, 71, 76, 84, 88, 93, 103, 107, 112, 119, 124, 128, 133, 140, 147, 151, 156, 163, 167, 172, 176, 181, 188, 192, 199, 203, 208, 215, 219, 224, 228, 232, 237, 244, 248, 253, 259, 263, 268, 275, 279, 284, 288

Offset: 1

Author

Clark Kimberling, Sep 25 2024

Keywords

• nonn
• base

Comments

Every positive integer is in exactly one of these sequences: A376357, A376358, A376359, or this sequence.

Conjecture: {a(n+1) - a(n) : n >= 1} = {4,5,6,7,8,9,10,11,13}. It has been checked that a(n+1) - a(n) is not 12 for 1<=n<=300000. (See related conjectures at A376357, A376358, and A376359.)

Crossrefs

Cf. A007961, A376354, A376357, A376358, A376359.

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]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* A376358 *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* this sequence *)
(* Peter J. C. Moses, Sep 20 2024 *)