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 A298002 Solution of the complementary equation a(n) = a(1)*b(n) - a(0)*b(n-1) + 4*n, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, b(2) = 5, and (b(n)) is the increasing sequence of positive integers not in (a(n)).  See Comments. 3
 1, 2, 14, 19, 24, 29, 34, 39, 44, 49, 54, 61, 65, 70, 75, 82, 86, 91, 96, 103, 107, 112, 117, 124, 128, 133, 138, 145, 149, 154, 159, 166, 170, 175, 180, 187, 191, 196, 201, 208, 212, 217, 222, 229, 233, 238, 243, 248, 253, 260, 264, 269, 276, 280, 285, 290 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A298000 for a guide to related sequences. Conjecture:  a(n) - n*L < 4 for n >= 1, where L = 3 + sqrt(5). LINKS Clark Kimberling, Table of n, a(n) for n = 0..10000 EXAMPLE a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, b(2) = 5, so that a(2) = 14. Complement: (b(n)) = (3,4,5,6,7,8,9,10,11,13,15,17,18,20...) MATHEMATICA a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5; a[n_] := a[n] = a[1]*b[n] - a[0]*b[n - 1] + 4 n; j = 1; While[j < 100, k = a[j] - j - 1; While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; k Table[a[n], {n, 0, k}]  (* A298002 *) CROSSREFS Cf. A297800, A297826, A297836, A297837. Sequence in context: A032476 A274062 A059205 * A217075 A187261 A101398 Adjacent sequences:  A297999 A298000 A298001 * A298003 A298004 A298005 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 08 2018 STATUS approved

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Last modified November 26 01:22 EST 2020. Contains 338631 sequences. (Running on oeis4.)