×

Characterization of the set of values \(f(n)=[n \alpha ], n=1,2,\dots \). (English) Zbl 0246.10005


MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11A63 Radix representation; digital problems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ahrens, W., Mathematische unterhaltungen und spiele, (1910), Teubner Leipzig, Bd. 1, 2 · JFM 31.0220.02
[2] Ball, W.W.R., (), 39
[3] Beatty, S.; Beatty, S., Problem 3177, Am. math. monthly, Am. math. monthly, 34, 159, (1927) · JFM 53.0198.06
[4] Coxeter, H.S.M., The Golden section, phyllotaxis and Wythoff’s game, Scripta math., 19, 135-143, (1953) · Zbl 0053.00702
[5] Domoryad, A.P., Mathematical games and pastimes, (1964), Pergamon Press Oxford, translated by H. Moss · Zbl 0116.00101
[6] Ky Fan, The Dunkel memorial problem book, Problem 4399, p. 57.
[7] Fraenkel, A.S., The bracket function and complementary sets of integers, Can. J. math., 21, 6-27, (1969) · Zbl 0172.32501
[8] A.S. Fraenkel and I. Borosh, A generalization of Wythoff’s game, J. Combinatorial Theory, to appear. · Zbl 0265.90065
[9] Newman, D.J.; Newman, D.J., Problem 5252, Am. math. monthly, Am. math. monthly, 72, 1144, (1965) · Zbl 0151.08103
[10] O’Beirne, T.H., Puzzles and paradoxes, (1965), Oxford University Press London · Zbl 0129.24201
[11] Olds, C.D., Continued fractions, (1963), Random House · Zbl 0123.25804
[12] Perron, O., Die lehre von den kettenbr├╝chen, (1929), Teubner Leipzig, Berlin, reprinted by Chelsea). · JFM 55.0262.09
[13] Stewart, B.M., Theory of numbers, (1964), MacMillan New York · Zbl 0122.29304
[14] Uspensky, J.V.; Heaslet, M.A., (), 98
[15] Vinogradov, I.M., (), 29, Problem 3
[16] Wythoff, W.A., A modification of the game of nim, Nieuw arch. wisk., 7, 199-202, (1907) · JFM 37.0261.03
[17] Yaglom, A.M.; Yaglom, I.M., Challenging mathematical problems with elementary solutions, Vol. 2, (1967), Holden-Day San Francisco, translated by J. McCawley Jr., revised and edited by B. Gordon · Zbl 0147.00102
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.