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Search: id:A097337
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| A097337 |
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Integer part of the edge of a cube that has space-diagonal n. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The first few terms are the same as A038128. However, A038128 is generated by Euler's constant = 0.5772156649015328606065120901..*n which is close to 1/sqrt(3)n = 0.5773502691896257645091487805..*n which generates this sequence. Euler/(1/sqrt(3)) = 0.9997668585341064519813571911.. and the equality fails in the 97-th term.
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REFERENCES
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The Universal Encyclopedia of Mathematics, English translation, 1964, p. 155.
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FORMULA
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Let e = edge. So sqrt(2)e is the diagonal of a face. Then n^2 = 2*e^2 + e^2 or n = sqrt(3)e and e = n/sqrt(3).
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PROGRAM
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(PARI) f(n) = for(x=1, n, s=x\sqrt(3); print1(s", "))
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CROSSREFS
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Sequence in context: A047783 A057358 A038128 this_sequence A163464 A139327 A076905
Adjacent sequences: A097334 A097335 A097336 this_sequence A097338 A097339 A097340
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Sep 17 2004
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