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a(n) is the "level" of even numbers.
The decomposition of even numbers into weight * level + gap is A005843(n) = A090369(n-1) * a(n) + 2 if a(n) > 0.
Rémi Eismann, Table of n, a(n) for n = 1..10000
For n = 3 we have A005843(2)/A090369(2)= 4 / 4 = 1; hence a(3) = 1.
For n = 24 we have A005843(23)/A090369(23)= 46 / 23 = 2; hence a(24) = 2.
Cf. A005843, A090369, A117078, A117563, A001223.
Sequence in context: A240039 A130127 A217982 * A098069 A173738 A135838
Adjacent sequences: A184724 A184725 A184726 * A184728 A184729 A184730
Rémi Eismann, Jan 20 2011