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 A297469 Solution (bb(n)) of the system of 3 complementary equations in Comments. 9
 2, 7, 11, 17, 22, 27, 31, 37, 41, 47, 51, 57, 62, 67, 71, 77, 82, 87, 91, 97, 102, 107, 111, 117, 121, 127, 131, 137, 142, 147, 151, 157, 161, 167, 171, 177, 182, 187, 191, 197, 201, 207, 211, 217, 222, 227, 231, 237, 242, 247, 251, 257, 262, 267, 271, 277 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Define sequences aa(n), bb(n), cc(n) recursively, starting with aa(0) = 1, bb(0) = 2, cc(0) = 3: aa(n) = least new; bb(n) = aa(n) + cc(n-1); cc(n) = least new; where "least new k" means the least positive integer not yet placed. *** The sequences aa,bb,cc partition the positive integers. It appears that cc = A047218 and that for every n >= 0, (1) 5*n - 1 - 2*aa(n) is in {0,1,2}, (2) (aa(n) mod 5) is in {1,2,4}, (3) 5*n - 3 - bb(n) is in {0,1} for every n >= 0; (4) (bb(n) mod 5) is in {1,2}. From N. J. A. Sloane, Nov 05 2019: (Start) Conjecture: For t >= 0, bb(2t) = 10t + 1 (+1 if binary expansion of t ends in an odd number of 0's), bb(2t+1) = 10t + 7. The first part may also be written as bb(2t) = 10t + 1 + A328789(t-1). (End) LINKS Clark Kimberling, Table of n, a(n) for n = 0..10000 [This is the sequence bb] EXAMPLE n: 0 1 2 3 4 5 6 7 8 9 10 aa: 1 4 6 9 12 14 16 19 21 24 26 bb: 2 7 11 17 22 27 31 37 41 47 51 cc: 3 5 8 10 13 15 18 20 23 25 28 MATHEMATICA z = 500; mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; b = {2}; c = {3}; Do[AppendTo[a, mex[Flatten[{a, b, c}], Last[a]]]; AppendTo[b, Last[a] + Last[c]]; AppendTo[c, mex[Flatten[{a, b, c}], Last[a]]], {z}]; Take[a, 100] (* A298468 *) Take[b, 100] (* A297469 *) Take[c, 100] (* A047218 *) (* Peter J. C. Moses, Apr 23 2018 *) CROSSREFS Cf. A299634, A298468 (aa), A047218 (cc), A328789. Sequence in context: A063205 A090613 A063097 * A356190 A168421 A038942 Adjacent sequences: A297466 A297467 A297468 * A297470 A297471 A297472 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 04 2018 EXTENSIONS Changed a,b,c to aa,bb,cc to avoid confusion caused by conflict with standard OEIS terminology. - N. J. A. Sloane, Nov 03 2019 STATUS approved

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Last modified May 24 15:12 EDT 2024. Contains 372778 sequences. (Running on oeis4.)