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 A022940 a(n) = a(n-1) + b(n-2) for n >= 3, a( ) increasing, given a(1) = 1, a(2) = 3; where b( ) is complement of a( ). 10
 1, 3, 5, 9, 15, 22, 30, 40, 51, 63, 76, 90, 106, 123, 141, 160, 180, 201, 224, 248, 273, 299, 326, 354, 383, 414, 446, 479, 513, 548, 584, 621, 659, 698, 739, 781, 824, 868, 913, 959, 1006, 1054, 1103, 1153, 1205, 1258, 1312, 1367, 1423, 1480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Clark Kimberling, Oct 30 2017: (Start) The complementary sequences a() and b() are uniquely determined by the titular equation and initial values. The initial values of each sequence in the following guide are a(0) = 1, a(2) = 3, b(0) = 2, b(1) = 4: here: a(n) = a(n-1) + b(n-2) [with a different offset] A294397: a(n) = a(n-1) + b(n-2) + 1; A294398: a(n) = a(n-1) + b(n-2) + 2; A294399: a(n) = a(n-1) + b(n-2) + 3; A294400: a(n) = a(n-1) + b(n-2) + n; A294401: a(n) = a(n-1) + b(n-2) + 2*n. (End) LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13. EXAMPLE a(1) = 1, a(2) = 3, b(1) = 2, b(2) = 4, so that a(3) = a(2) + a(1) + b(2) = 5. Complement: {b(n)} = {2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, ...} MATHEMATICA Fold[Append[#1, #1[[-1]] + Complement[Range[Max@#1 + 1], #1][[#2]]] &, {1, 3}, Range[50]] (* Ivan Neretin, Apr 04 2016 *) CROSSREFS Cf. A005228 and references therein. Cf. A293076, A293765, A294381. Sequence in context: A029518 A061954 A095039 * A025207 A027688 A118403 Adjacent sequences: A022937 A022938 A022939 * A022941 A022942 A022943 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 5 13:26 EST 2022. Contains 358586 sequences. (Running on oeis4.)