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

1,1

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.)

Links

Table of n, a(n) for n=1..59.

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 *)

Crossrefs

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

Sequence in context: A071835 A308416 A010429 * A140282 A161757 A134376

Adjacent sequences: A376354 A376355 A376356 * A376358 A376359 A376360

Keyword

nonn,base

Author

Clark Kimberling, Sep 25 2024

Status

approved