

A097337


Integer part of the edge of a cube that has spacediagonal n.


7



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
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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.


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


CROSSREFS

Cf. A020760 (1/sqrt(3)).
Sequence in context: A194208 A057358 A038128 * A263574 A278496 A163464
Adjacent sequences: A097334 A097335 A097336 * A097338 A097339 A097340


KEYWORD

nonn


AUTHOR

Cino Hilliard, Sep 17 2004


STATUS

approved



