A107227 -id:A107227 - cp's OEIS frontend

A107016 Number of odd terms in Zeckendorf representation of n.

1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 3, 4, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3

Offset: 1

Reinhard Zumkeller, May 09 2005

nonn

a(n) = A007895(n) - A107015(n).

a(A107227(n)) = 0. - Reinhard Zumkeller, May 15 2005

			n = 77 = 55+21+1 -> a(77) = #{1, 21, 55} = 3;
n = 88 = 55+21+8+3+1 -> a(88) = #{1, 3, 21, 55} = 4;
n = 99 = 89+8+2 -> a(99) = #{89} = 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Zeckendorf Representation

Cf. A000045.
Cf. A107224, A107225, A107226.
Cf. A035516.

a107016 = length . filter odd . a035516_row
-- Reinhard Zumkeller, Mar 10 2013

A107228 Numbers having no even terms in their Zeckendorf representation.

Original entry on oeis.org

1, 3, 4, 5, 6, 13, 14, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 55, 56, 58, 59, 60, 61, 68, 69, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 89, 90, 92, 93, 94, 95, 102, 103, 105, 106, 107, 108, 110, 111, 113, 114, 115, 116, 233, 234, 236, 237, 238, 239, 246, 247, 249, 250

Offset: 1

Reinhard Zumkeller, May 15 2005

nonn

A107015(a(n))=0, A107016(a(n))>0; subsequence of A107224.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Zeckendorf Representation

Cf. A107227.

Cf. A035516, A014437, A014445, A011655.

a107228 n = a107228_list !! (n-1)
a107228_list = filter ((all odd) . a035516_row) [1..]
-- Reinhard Zumkeller, Mar 10 2013

cp's OEIS Frontend

A107016 Number of odd terms in Zeckendorf representation of n.

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