The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A298111 Solution b( ) of the complementary equation a(n) = a(1)*b(n) - a(0)*b(n-1) + 2*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. 2
 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 25, 26, 28, 30, 31, 32, 33, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 49, 51, 52, 53, 54, 56, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 78, 79, 81, 82, 83, 84, 86, 87, 88, 90, 92, 93 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values.  The solution a( ) is given at A298000.  See A297830 for a guide to related sequences. Conjecture:  1/5 < a(n) - n*sqrt(2) < 3 for n >= 1. LINKS Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13. MATHEMATICA a = 1; a = 2; b = 3; b = 4; b = 5; a[n_] := a[n] = a*b[n] - a*b[n - 1] + 2 n; j = 1; While[j < 80000, k = a[j] - j - 1; While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; k u = Table[a[n], {n, 0, k}]; (* A298000 *) v = Table[b[n], {n, 0, k}]; (* A298111 *) Take[u, 50] Take[v, 50] CROSSREFS Cf. A297830, A298000. Sequence in context: A258187 A039237 A039181 * A299534 A026454 A026458 Adjacent sequences:  A298108 A298109 A298110 * A298112 A298113 A298114 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 09 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 December 5 06:44 EST 2020. Contains 338944 sequences. (Running on oeis4.)