This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A258048 Nonhomogeneous Beatty sequence: ceiling((n + 1/2)*Pi/(Pi- 1)) 2
 1, 3, 4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 58, 60, 61, 63, 64, 66, 67, 69, 70, 72, 73, 75, 76, 78, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Let r = Pi, s = r/(r-1), and t = 1/2. Let R be the ordered set {floor[(n + t)*r] : n is an integer} and let S be the ordered set {floor[(n - t)*s : n is an integer}; thus, R = (..., -10, -9, -7, -6, -4, -3, -1, 0, 2, 3, 5, 6, 8, ...). S = (..., -15, -11, -8, -5, -2, 1, 4, 7, 10, 14, 17, 20, ...) By Fraenkel's theorem (Theorem XI in the cited paper); R and S partition the integers. R is the set of integers n such that (cos n)*(cos(n + 1)) < 0; S is the set of integers n such that (cos n)*(cos(n + 1)) > 0. A246046 = (2,3,6,6,8,...), positive terms of R; A062389 = (1,4,7,10,14,17,...), positive terms of S; A258048 = (1,3,4,6,7,9,10,...), - (nonpositive terms of R). A257984 = (2,5,8,11,15,...), - (negative terms of S); A062389 and A246046 partition the positive integers, and A258048 and A257984 partition the nonnegative integers. LINKS Clark Kimberling, Table of n, a(n) for n = 0..10000 A. S. Fraenkel, The bracket function and complementary sets of integers, Canadian J. of Math. 21 (1969) 6-27. FORMULA a(n) = ceiling((n + 1/2)*Pi/(Pi - 1)). MATHEMATICA Table[Ceiling[(n - 1/2) Pi], {n, 1, 120}] (* A257984 *) Table[Ceiling[(n + 1/2) Pi/(Pi - 1)], {n, 0, 120}]  (* A258048 *) CROSSREFS Cf. A257984 (complement), A246046, A062380, A258833. Sequence in context: A186495 A184746 A186227 * A185543 A026322 A049624 Adjacent sequences:  A258045 A258046 A258047 * A258049 A258050 A258051 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 15 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)