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A094591 a(0) = 1; a(n) = n + (largest element of {a} <= n).

%I A094591 #25 Nov 19 2021 02:48:04
%S A094591 1,2,4,5,8,10,11,12,16,17,20,22,24,25,26,27,32,34,35,36,40,41,44,45,
%T A094591 48,50,52,54,55,56,57,58,64,65,68,70,72,73,74,75,80,82,83,84,88,90,91,
%U A094591 92,96,97,100,101,104,105,108,110,112,114,116,117,118,119,120,121,128,130
%N A094591 a(0) = 1; a(n) = n + (largest element of {a} <= n).
%C A094591 A self-describing sequence. Pick any number n; this n says: "There are n terms in the sequence which are < 2n". This sequence is the slowest increasing one with this property. See comments on A037988. - _Eric Angelini_, Jun 15 2007
%H A094591 Michael De Vlieger, <a href="/A094591/b094591.txt">Table of n, a(n) for n = 0..10000</a>
%H A094591 Jon Maiga, <a href="http://sequencedb.net/s/A094591">Computer-generated formulas for A094591</a>, Sequence Machine.
%F A094591 From _Andrey Zabolotskiy_, Oct 28 2021: (Start)
%F A094591 a(n) = A037988(n-1) + 1. [Conjectured by the original author, apparently proved by Eric Angelini.]
%F A094591 The first differences are A272729. [discovered by Sequence Machine] (End)
%t A094591 Block[{a = {1}}, Do[AppendTo[a, i + Last@ TakeWhile[a, # <= i &]], {i, 65}]; a] (* _Michael De Vlieger_, Sep 04 2017 *)
%o A094591 (Python)
%o A094591 def aupton(nn):
%o A094591     alst = [1]
%o A094591     for n in range(1, nn+1):
%o A094591         alst.append(n + max(k for k in alst if k <= n))
%o A094591     return alst
%o A094591 print(aupton(65)) # _Michael S. Branicky_, Oct 28 2021
%Y A094591 Cf. A037988, A272729.
%K A094591 nonn,easy
%O A094591 0,2
%A A094591 _Leroy Quet_, Jun 07 2004
%E A094591 More terms from _Vladeta Jovovic_, Jun 11 2004