A064875 -id:A064875 - cp's OEIS frontend

A064873 First of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = a(n)^2 + A064874(n)^2 + A064875(n)^2 + A064876(n)^2.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset: 0

Reinhard Zumkeller, Oct 10 2001

nonn

A072401(n) = A057427(a(n)).

For k<112: a(n)=A072401(n), but A072401(112) = 1<>a(112)=2, as also A072401(112 - 1) = 1.

			a(25) = 0: 25 = a(25)^2 + A064874(25)^2 + A064875(25)^2 + A064876(25)^2 = 0 + 0 + 0 + 25 and the other decompositions (0, 0, 3, 4) and (1, 2, 2, 4) are greater than (0, 0, 0, 5).

Eric Weisstein's World of Mathematics, Square Numbers.
Index entries for sequences related to sums of squares.

Cf. A064874, A064875, A064876, A071374.

A064874 Second of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = A064873(n)^2 + a(n)^2 + A064875(n)^2 + A064876(n)^2.

Original entry on oeis.org

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

Offset: 0

Reinhard Zumkeller, Oct 10 2001

nonn

			a(19) = 1: 19 = A064873(19)^2 + a(19)^2 + A064875(19)^2 + A064876(19)^2 = 0 + 1 + 9 + 9 and the other decomposition (1, 1, 1, 4) is greater than (0, 1, 3, 3).

Cf. A064873, A064875, A064876, A064877.

A064876 Last of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = A064873(n)^2 + A064874(n)^2 + A064875(n)^2 + a(n)^2.

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 6, 6, 6, 6, 4, 7, 7, 7, 6, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6, 6, 8, 8, 8, 7, 8, 8, 6, 6, 6, 8, 7, 7, 6, 8, 7, 7, 8, 9, 9, 9, 8, 9, 9, 9, 6, 8, 9, 9, 9, 8, 9, 9, 8, 9, 7, 7, 10, 10, 10

Offset: 0

Reinhard Zumkeller, Oct 10 2001

nonn

			a(18) = 3: 18 = A064873(18)^2 + A064874(18)^2 + A064875(18)^2 + a(18)^2 = 0 + 0 + 9 + 9 and the other decompositions (0, 1, 1, 4) and (1, 2, 2, 3) are greater than (0, 0, 3, 3).

Cf. A064873, A064874, A064875, A064877.

A064877 a(n) = n - (A064873(n) + A064874(n) + A064875(n) + A064876(n)).

Original entry on oeis.org

0, 0, 0, 0, 2, 2, 2, 2, 4, 6, 6, 6, 6, 8, 8, 8, 12, 12, 12, 12, 14, 14, 14, 14, 16, 20, 20, 20, 20, 22, 22, 22, 24, 24, 26, 26, 30, 30, 30, 30, 32, 32, 32, 32, 34, 36, 36, 36, 36, 42, 42, 42, 42, 44, 44, 44, 44, 46, 48, 48, 48, 50, 50, 50, 56, 56, 56, 54, 58, 58, 56, 56, 60, 62

Offset: 0

Reinhard Zumkeller, Oct 10 2001

nonn

Cf. A064873, A064874, A064875, A064876.

cp's OEIS Frontend

A064873 First of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = a(n)^2 + A064874(n)^2 + A064875(n)^2 + A064876(n)^2.

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A064874 Second of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = A064873(n)^2 + a(n)^2 + A064875(n)^2 + A064876(n)^2.

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A064876 Last of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = A064873(n)^2 + A064874(n)^2 + A064875(n)^2 + a(n)^2.

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A064877 a(n) = n - (A064873(n) + A064874(n) + A064875(n) + A064876(n)).

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