A097337 Integer part of the edge of a cube that has space-diagonal n.

0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43

Offset

1,4

Comments

The first few terms are the same as A038128. However, A038128 is generated by Euler's constant = 0.5772156649015328606065120901..., which is close but not equal to 1/sqrt(3) = 0.5773502691896257645091487805..., which generates this sequence. Euler/(1/sqrt(3)) = 0.9997668585341064519813571911... and the equality fails in the 97th term.

The integers k such that a(k) = a(k+1) give A054406. - Michel Marcus, Nov 01 2021

References

The Universal Encyclopedia of Mathematics, English translation, 1964, p. 155.

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..1000

Index entries for sequences related to Beatty sequences

Formula

Let L be the length of the edges. Then sqrt(2)*L is the diagonal of a face. Whence n^2 = 2*L^2 + L^2, or n = sqrt(3)*L and L = n/sqrt(3).

Prog

(PARI) f(n) = for(x=1, n, s=x\sqrt(3); print1(s", ")); s
(PARI) a(n)=sqrtint(n^2\3) \\ Charles R Greathouse IV, Nov 01 2021

Crossrefs

Cf. A020760 (1/sqrt(3)), A054406.

Sequence in context: A194208 A057358 A038128 * A263574 A366701 A278496

Adjacent sequences: A097334 A097335 A097336 * A097338 A097339 A097340

Keyword

nonn,easy

Author

Cino Hilliard, Sep 17 2004

Status

approved