A376358 Positions of numbers in A007961 that end in 1.

1, 5, 10, 14, 17, 21, 26, 30, 35, 37, 41, 46, 50, 54, 59, 63, 65, 69, 74, 78, 82, 86, 91, 95, 98, 101, 105, 110, 114, 117, 122, 126, 131, 135, 138, 142, 145, 149, 154, 158, 161, 165, 170, 174, 179, 183, 186, 190, 195, 197, 201, 206, 210, 213, 217, 222, 226

Offset: 1

Author

Clark Kimberling, Sep 25 2024

Keywords

• nonn
• base

Comments

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

Conjecture: {a(n+1) - a(n) : n >= 1} = {2,3,4,5,6,7}. (See related conjectures at A376357, A376359, and A376360.)

Crossrefs

Cf. A007961, A376354, A376357, 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]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* this sequence *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* A376360 *)
(* Peter J. C. Moses, Sep 20 2024 *)