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%I #7 Sep 22 2024 18:07:25
%S 3,6,9,10,13,15,18,21,24,27,28,31,34,36,39,42,45,48,51,54,55,58,61,64,
%T 65,66,69,72,75,76,78,81,84,87,88,91,94,97,100,101,104,105,108,111,
%U 114,115,118,120,123,126,129,130,133,135,136,139,142,145,146,149
%N Numbers that end in 0 when written in base of triangular numbers (cf. A000462).
%C Every positive integer is in exactly one of the following sequences: this sequence, A376355, or A376356.
%C Conjecture: {a(n+1) - a(n) : n >= 1} = {1, 2, 3}. (See related conjectures at A376355 and A376356.)
%t 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 t3 = Map[a[#, 3] &, Range[200]]; (* A000462 *)
%t m = Mod[t3, 10]
%t Table[Flatten[Position[m, r]], {r, 0, 2}]
%t p0 = Flatten[Position[m, 0]] (* this sequence *)
%t p1 = Flatten[Position[m, 1]] (* A376355 *)
%t p2 = Flatten[Position[m, 2]] (* A376356 *)
%t (* _Peter J. C. Moses_, Sep 20 2024 *)
%Y Cf. A000462, A376355, A376356, A376357.
%K nonn,base
%O 1,1
%A _Clark Kimberling_, Sep 22 2024