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 A297291 Solution (a(n)) of the system of 3 complementary equations in Comments. 3
 1, 4, 5, 9, 12, 13, 16, 17, 21, 22, 27, 28, 31, 32, 37, 38, 41, 44, 47, 48, 51, 52, 57, 58, 61, 62, 67, 68, 71, 72, 77, 78, 81, 84, 85, 89, 90, 93, 97, 98, 101, 104, 107, 108, 111, 112, 117, 118, 121, 122, 127, 128, 131, 132, 137, 138, 141, 144, 147, 148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Define sequences a(n), b(n), c(n) recursively: a(n) = least new; b(n) = least new > = a(n) + 2; c(n) = a(n) + b(n) - 2; where "least new k" means the least positive integer not yet placed. *** The sequences a,b,c partition the positive integers. *** Conjectures:  for n >=0, 0 <= 5*n + 4 - 2*a(n) <= 5, 0 <= 5*n + 8 - 2*b(n) <= 4, 0 <= c(n) - 5n <= 4. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 EXAMPLE n:   0   1   2   3   4   5   6   7   8   9  10 a:   1   4   5   9  12  13  16  17  21  27  28 b:   3   6   7  11  14  15  19  20  23  25  29 c:   2   8  10  18  24  26  33  35  42  45  54 MATHEMATICA z = 300; mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = b = c = {}; Do[{AppendTo[a,     mex[Flatten[{a, b, c}], If[Length[a] == 0, 1, Last[a]]]],    AppendTo[b, mex[Flatten[{a, b, c}], Last[a] + 2]],    AppendTo[c, Last[a] + Last[b] - 2]}, {z}]; Take[a, 100]  (* A297291 *) Take[b, 100]  (* A297292 *) Take[c, 100]  (* A297293 *) (* Peter J. C. Moses,  Apr 23 2018 *) CROSSREFS Cf. A299634, A297292, A297293. Sequence in context: A319606 A230239 A194154 * A269741 A047610 A126004 Adjacent sequences:  A297288 A297289 A297290 * A297292 A297293 A297294 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 24 2018 STATUS approved

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Last modified September 20 03:47 EDT 2021. Contains 347577 sequences. (Running on oeis4.)