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 A036415 Values of k for which there are no empty intervals when fractional part(m*phi) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions. 2
 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence contains the Fibonacci numbers A000045. If fact, for all known terms with n > 10, a(n) = A000045(n-3). - Eric W. Weisstein, Apr 17 2024 No others terms with n <= 10^6. - Eric W. Weisstein, Apr 28 2024 REFERENCES H. Steinhaus, Mathematical Snapshots, 3rd American ed., New York: Oxford University Press, pp. 48-49, 1983. LINKS Table of n, a(n) for n=1..33. Eric Weisstein's World of Mathematics, Equidistributed Sequence. Eric Weisstein's World of Mathematics, Golden Ratio. MATHEMATICA With[{f = FractionalPart[GoldenRatio Range[1000]]}, Position[Table[Count[BinCounts[Take[f, n], {0., 1, 1/n}], 0], {n, Length[f]}], 0]] // Flatten (* Eric W. Weisstein, Apr 27 2024 *) CROSSREFS Cf. A000045, A036414. Sequence in context: A241089 A186445 A080078 * A054961 A086736 A175773 Adjacent sequences: A036412 A036413 A036414 * A036416 A036417 A036418 KEYWORD nonn,more AUTHOR Eric W. Weisstein EXTENSIONS a(27)-a(29) from Sean A. Irvine, Oct 31 2020 a(30)-a(31) from Eric W. Weisstein, Apr 18-19 2024 a(32)-a(33) from Eric W. Weisstein, Apr 28 2024 STATUS approved

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Last modified August 14 00:08 EDT 2024. Contains 375146 sequences. (Running on oeis4.)