The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A298869 Solution (b(n)) of the system of 3 complementary equations in Comments. 3
 2, 5, 7, 10, 12, 16, 20, 22, 25, 28, 31, 36, 38, 40, 43, 47, 50, 51, 56, 60, 63, 66, 68, 71, 76, 78, 81, 85, 86, 89, 91, 95, 99, 103, 106, 109, 110, 114, 117, 121, 124, 128, 133, 135, 137, 139, 142, 146, 148, 151, 154, 156, 159, 164, 167, 170, 174, 176, 178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Define sequences a(n), b(n), c(n) recursively, starting with a(0) = 1, b(0) = 2: a(n) = least new; b(n) = least new k >= a(n) + n; c(n) = a(n) + b(n); where "least new k" means the least positive integer not yet placed. *** The sequences a,b,c partition the positive integers. Let x = be the greatest solution of 1/x + 1/(x+1) + 1/(2x+1) = 1. Then x = 1/3 + (2/3)*sqrt(7)*cos((1/3)*arctan((3*sqrt(111))/67)); x = 2.07816258732933084676..., and a(n)/n - > x, b(n)/n -> x+1, and c(n)/n -> 2x+1. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 EXAMPLE n: 0 1 2 3 4 5 6 7 8 9 a: 1 4 6 8 11 14 15 17 19 21 b: 2 5 7 10 12 16 20 22 25 28 c: 3 9 13 18 23 30 35 39 44 49 MATHEMATICA z = 400; mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; b = {2}; c = {}; AppendTo[c, Last[a] + Last[b]]; n = 0; Do[{n++, AppendTo[a, mex[Flatten[{a, b, c}], 1]], AppendTo[b, mex[Flatten[{a, b, c}], a[[n]] + n]], AppendTo[c, Last[a] + Last[b]]}, {z}]; Take[a, 100] (* A298868 *) Take[b, 100] (* A298869 *) Take[c, 100] (* A298870 *) (* Peter J. C. Moses, Apr 08 2018 *) CROSSREFS Cf. A299634, A298868, A298870. Sequence in context: A206807 A182773 A346155 * A219666 A026340 A331833 Adjacent sequences: A298866 A298867 A298868 * A298870 A298871 A298872 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 17 2018 STATUS approved

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

Last modified September 13 17:14 EDT 2024. Contains 375910 sequences. (Running on oeis4.)