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A379413 a(n) = n + floor(n*r/t) + floor(n*s/t), where r = e^(1/4), s = e^(1/2), t = e^(3/4).

%I A379413 #8 Jan 20 2025 17:11:16
%S A379413 1,4,6,9,11,13,16,18,21,23,25,28,30,32,35,37,40,42,44,47,49,52,53,56,
%T A379413 59,61,64,65,68,71,73,75,78,80,83,85,87,90,92,95,96,99,102,104,107,
%U A379413 108,111,114,116,118,120,123,126,128,130,132,135,138,139,142,144
%N A379413 a(n) = n + floor(n*r/t) + floor(n*s/t), where r = e^(1/4), s = e^(1/2), t = e^(3/4).
%C A379413 This sequence and A379411 and A379412 partition the positive integers; see A378142 for a proof.
%F A379413 a(n) = n + floor(n/r) + floor(n*r^2), where r = e^(1/4).
%t A379413 r = E^(1/4); s = E^(1/2); t = E^(3/4);
%t A379413 Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379411 *)
%t A379413 Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379412 *)
%t A379413 Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379413 *)
%Y A379413 Cf. A378142, A379411, A379412.
%Y A379413 Cf. A092042, A019774, A331501.
%K A379413 nonn
%O A379413 1,2
%A A379413 _Clark Kimberling_, Jan 18 2025