A083054 -id:A083054 - cp's OEIS frontend

A083055 a(n) = cardinality{ k<=n / A083054(k)=1}.

1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 25, 25

Offset: 1

Benoit Cloitre, Apr 18 2003

nonn

Boris Gourevitch, Graph of A083057

Cf. A083038, A083054, A083056, A083057.

{a(n)=if(n<1,0, sum(k=1,n,sqrtint(3*k^2)-3*sqrtint(k^2\3)==1))} /* Michael Somos, Aug 31 2006 */

a(n) = n/3 + O(n) (it seems O(n) could be replaced with O(log(n))).

A083057 A fractal sequence.

Original entry on oeis.org

2, 3, 3, 2, 0, 0, -1, 0, 0, -1, 0, 0, 2, 3, 6, 8, 9, 12, 14, 18, 21, 23, 24, 24, 26, 27, 30, 32, 33, 33, 32, 33, 33, 35, 36, 36, 38, 39, 42, 44, 45, 45, 44, 45, 45, 47, 48, 48, 47, 45, 45, 44, 45, 45, 44, 42, 39, 38, 36, 36, 35, 33, 33, 32, 33, 33, 32, 30, 27, 26, 24, 24, 23, 21, 18, 14, 12, 9, 8, 6, 3, 2, 0, 0, -1, 0, 0, -1, 0, 0, 2, 3, 3, 2, 0

Offset: 1

Benoit Cloitre, Apr 18 2003

sign

Boris Gourevitch, Graph of A083057

Cf. A083038, A083054, A083055, A083056.

a(n)=sum(k=1, n, A083056(k))

A083056 a(n) = 3*A083055(n)-n.

Original entry on oeis.org

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

Offset: 1

Benoit Cloitre, Apr 18 2003

sign

Boris Gourevitch, Graph of A083057

Cf. A083038, A083054, A083055, A083057.

cp's OEIS Frontend

A083055 a(n) = cardinality{ k<=n / A083054(k)=1}.

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A083057 A fractal sequence.

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Formula

A083056 a(n) = 3*A083055(n)-n.

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