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A379411 a(n) = n + floor(n*s/r) + floor(n*t/r), where r = e^(1/4), s = e^(1/2), t = e^(3/4).

%I A379411 #10 Jan 20 2025 17:10:50
%S A379411 3,7,10,15,19,22,26,31,34,38,43,46,50,54,58,62,66,70,74,77,81,86,89,
%T A379411 93,98,101,105,109,113,117,121,125,129,133,136,141,145,148,153,156,
%U A379411 160,164,168,172,176,180,184,188,191,196,200,203,208,212,215,219,223
%N A379411 a(n) = n + floor(n*s/r) + floor(n*t/r), where r = e^(1/4), s = e^(1/2), t = e^(3/4).
%C A379411 This sequence and A379412 and A379413 partition the positive integers; see A184812 for a proof. For each k in A000027, write "a" if k=A379411(n) for some n, "b" if k=A379412(n) for some n, and "c" if k=A379413(n) for some n. Concatenating these letters for k = 1,2,3,... spells the following infinite word:
%C A379411 cbacbcabcacbcbacbcabcacbcabcbcacbacbcabcbcacbacbcabccabcbacbcabccabcbacbcacbacbcabcbcacbacbcabccbacbacbcabccabcbacbcacbcabcbacbcacbcabcabccbacb...
%F A379411 a(n) = n + floor(n*r) + floor(n*r^2), where r = e^(1/4).
%t A379411 r = E^(1/4); s = E^(1/2); t = E^(3/4);
%t A379411 Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379411 *)
%t A379411 Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379412 *)
%t A379411 Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379413 *)
%Y A379411 Cf. A184812, A379412, A379413.
%Y A379411 Cf. A092042, A019774, A331501.
%K A379411 nonn
%O A379411 1,1
%A A379411 _Clark Kimberling_, Jan 18 2025