A298644 -id:A298644 - cp's OEIS frontend

1, 4, 7, 9, 16, 28, 31, 33, 36, 39, 57, 64, 73, 112, 124, 127, 129, 132, 135, 144, 156, 159, 225, 228, 231, 249, 256, 265, 289, 292, 295, 313, 448, 457, 496, 508, 511, 513, 516, 519, 528, 540, 543, 576, 585, 624, 636, 639, 897, 900

Offset: 1

Clark Kimberling

From Emeric Deutsch, Jan 27 2018: (Start)
Also the indices of the compositions whose parts alternate: odd, even, odd, ... . For the definition of the index of a composition see A298644.
For example, 57 is in the sequence since its binary form is 111001 and the composition [3,2,1] has parts: odd, even, odd. 59 is not in the sequence since its binary form is 111011 and the composition [3,1,2] has parts: odd, odd, even. The command c(n) from the Maple program yields the composition having index n. (End)

Cf. A298644, A101211.

Runs := proc (L) local j, r, i, k: j := 1: r[j] := L[1]: for i from 2 to nops(L) do if L[i] = L[i-1] then r[j] := r[j], L[i] else j := j+1: r[j] := L[i] end if end do: [seq([r[k]], k = 1 .. j)] end proc: RunLengths := proc (L) map(nops, Runs(L)) end proc: c := proc (n) ListTools:-Reverse(convert(n, base, 2)): RunLengths(%) end proc: A := {}: for n to 900 do if `and`(type(c(n)[1], odd) = true, type(product(c(n)[j]-c(n)[j+1], j = 1 .. nops(c(n))-1), odd)) then A := `union`(A, {n}) else  end if end do: A; # most of the Maple program is due to W. Edwin Clark. # Emeric Deutsch, Jan 27 2018

from itertools import groupby
def ok(n): return all(len(list(g))%2 != i%2 for i, (k, g) in enumerate(groupby(bin(n)[2:])))
print([i for i in range(1, 901) if ok(i)]) # Michael S. Branicky, Jan 04 2021

cp's OEIS Frontend

A044903 Base-2 run lengths alternate: odd, even, odd, ...

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