The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297832 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*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. 5
 1, 2, 7, 10, 13, 18, 20, 25, 27, 32, 34, 37, 40, 45, 49, 51, 54, 57, 62, 66, 68, 71, 74, 79, 83, 85, 90, 92, 97, 99, 102, 105, 110, 112, 115, 120, 124, 126, 131, 133, 138, 140, 143, 146, 151, 153, 156, 161, 165, 167, 172, 174, 179, 181, 184, 187, 192, 194 (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 A297830 for a guide to related sequences. a(n) - (2+sqrt(2))*n < 2 for n >= 1. 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, so that a(2) = 7. Complement: (b(n)) = (3,4,5,7,8,10,12,13,15,17,18,19,...) MATHEMATICA a = 1; a = 2; b = 3; b = 4; a[n_] := a[n] = a*b[n - 1] - a*b[n - 2] + 2 n - 2; 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}]  (* A297832 *) CROSSREFS Cf. A297826, A297830. Sequence in context: A029904 A026364 A203621 * A003158 A130336 A303741 Adjacent sequences:  A297829 A297830 A297831 * A297833 A297834 A297835 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 04 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 19 08:05 EDT 2021. Contains 347556 sequences. (Running on oeis4.)