cp's OEIS Frontend

A297998 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + floor(5*n/2), where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.

%I A297998 #5 Feb 06 2018 19:28:16
%S A297998 1,2,10,13,17,20,24,27,33,35,41,43,47,52,55,60,63,66,72,74,80,82,86,
%T A297998 89,93,98,103,105,109,112,116,121,126,128,132,137,140,143,147,152,155,
%U A297998 160,163,166,170,175,178,183,186,191,194,197,201,204,210,214,217
%N A297998 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + floor(5*n/2), where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)).  See Comments.
%C A297998 The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values.
%H A297998 Clark Kimberling, <a href="/A297998/b297998.txt">Table of n, a(n) for n = 0..10000</a>
%e A297998 a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, so that a(2) = 10.
%e A297998 Complement: (b(n)) = (3,4,5,6,7,8,9,11,12,14,15,16,18,19,21,...)
%t A297998 a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
%t A297998 a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + Floor[5/2];
%t A297998 j = 1; While[j < 100, k = a[j] - j - 1;
%t A297998  While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; k
%t A297998 Table[a[n], {n, 0, k}]  (* A297998 *)
%Y A297998 Cf. A297826, A297830, A297836.
%K A297998 nonn,easy
%O A297998 0,2
%A A297998 _Clark Kimberling_, Feb 04 2018