A379413 - OEIS

%I #8 Jan 20 2025 17:11:16

%S 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 59,61,64,65,68,71,73,75,78,80,83,85,87,90,92,95,96,99,102,104,107,

%U 108,111,114,116,118,120,123,126,128,130,132,135,138,139,142,144

%N 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 This sequence and A379411 and A379412 partition the positive integers; see A378142 for a proof.

%F a(n) = n + floor(n/r) + floor(n*r^2), where r = e^(1/4).

%t r = E^(1/4); s = E^(1/2); t = E^(3/4);

%t Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379411 *)

%t Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379412 *)

%t Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379413 *)

%Y Cf. A378142, A379411, A379412.

%Y Cf. A092042, A019774, A331501.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 18 2025