A270362 Running maxima of Stern's diatomic sequence.

0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21

Offset: 0

Author

Jeffrey Shallit, Mar 15 2016

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Catherine Mary Kenyon, The Calkin-Wilf Tree and Its Various Properties, Master's Thesis, Clemson University (2019), 3075.

Crossrefs

Distinct elements are A212289. Cf. A002487, A212288.

Programs

Mathematica

FoldList[Max, Nest[Append[#1, If[OddQ[#2], #1[[(#2 + 1)/2]], #1[[#2/2]] + #1[[(#2 + 2)/2]] ]] & @@ {#, Length@ # + 1} &, {0, 1}, 90]] (* Michael De Vlieger, Jul 10 2019 *)

Formula

a(n) = max_{0 <= i <= n} A002487(i).