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A080588 a(n) is the smallest nonnegative integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 4n.

%I A080588 #30 Jun 05 2025 08:20:01
%S A080588 0,2,4,5,8,12,13,14,16,17,18,19,20,24,28,29,32,36,40,44,48,49,50,51,
%T A080588 52,53,54,55,56,60,61,62,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
%U A080588 79,80,84,88,92,96,100,104,108,112,113,114,115,116,120,124,125
%N A080588 a(n) is the smallest nonnegative integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 4n.
%C A080588 Equivalently: a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is a multiple of 4".
%C A080588 The sequence of even numbers shares many of the properties of this sequence.
%H A080588 Mathieu Gouttenoire, <a href="/A080588/b080588.txt">Table of n, a(n) for n = 0..100000</a>
%H A080588 J.-P. Allouche, N. Rampersad, and Jeffrey Shallit, <a href="http://dx.doi.org/10.1007/s00010-004-2750-x">On integer sequences whose first iterates are linear</a>, Aequationes Math. 69 (2005), 114-127.
%H A080588 Benoit Cloitre, N. J. A. Sloane, and M. J. Vandermast, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A080588 Benoit Cloitre, N. J. A. Sloane, and M. J. Vandermast, <a href="https://arxiv.org/abs/math/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.
%H A080588 <a href="/index/Aa#aan">Index entries for sequences of the a(a(n)) = 2n family</a>.
%F A080588 a(a(n)) = 4n. a(2^k) = 2^(k+1).
%F A080588 a(n) = A080591(n-1) + 1, n >= 1.
%Y A080588 Cf. A079000, A080591, A080589.
%K A080588 nonn,easy,nice
%O A080588 0,2
%A A080588 _N. J. A. Sloane_, Feb 23 2003