cp's OEIS Frontend

A376355 Numbers that end in 1 when written in base of triangular numbers (cf. A000462).

%I A376355 #7 Sep 22 2024 18:18:21
%S A376355 1,4,7,11,14,16,19,22,25,29,32,35,37,40,43,46,49,52,56,59,62,67,70,73,
%T A376355 77,79,82,85,89,92,95,98,102,106,109,112,116,119,121,124,127,131,134,
%U A376355 137,140,143,147,150,152,154,157,160,164,167,169,172,175,178,182
%N A376355 Numbers that end in 1 when written in base of triangular numbers (cf. A000462).
%C A376355 Every positive integer is in exactly one of the following sequences: A376355, this sequence, or A376356.
%C A376355 Conjecture: {a(n+1) - a(n) : n >= 1} = {2,3,4,5,6}. (See related conjectures at A376354 and A376356.)
%t A376355 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]]]
%t A376355 t3 = Map[a[#, 3] &, Range[200]]; (* A000462 *)
%t A376355 m = Mod[t3, 10]
%t A376355 Table[Flatten[Position[m, r]], {r, 0, 2}]
%t A376355 p0 = Flatten[Position[m, 0]]  (* A376354 *)
%t A376355 p1 = Flatten[Position[m, 1]]  (* this sequence *)
%t A376355 p2 = Flatten[Position[m, 2]]  (* A376356 *)
%t A376355 (* _Peter J. C. Moses_, Sep 20 2024 *)
%Y A376355 Cf. A000462, A376354, A376356, A376357.
%K A376355 base,nonn
%O A376355 1,2
%A A376355 _Clark Kimberling_, Sep 22 2024