The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A304799 Solution (a(n)) of the complementary equation a(n) = b(n) + b(2n); see Comments. 19
 2, 7, 10, 14, 18, 23, 26, 31, 34, 38, 43, 46, 50, 55, 59, 62, 66, 71, 74, 79, 82, 86, 90, 95, 98, 103, 106, 110, 115, 118, 122, 126, 131, 134, 139, 142, 146, 151, 154, 158, 162, 167, 170, 174, 179, 182, 187, 191, 194, 199, 203, 206, 210, 215, 218, 223, 226 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Define complementary sequences a(n) and b(n) recursively: both are strictly increasing, b(0) = 1, and a(n) = b(n) + b(2n) for n >= 0. Empirically, (1) {a(n) - 4*n: n >= 0} = {2,3} and {3*b(n) - 4*n: n >= 0} = {2,3,4,5}. (2) If the equation for a(n) is generalized to a(n) = b(h*n) + b(k*n), where 1 <= h < k, then {a(n) - (h + k + 1)*n: n >= 0} = {2,3} and {(h + k)*b(n) - (h + k + 1)*n : n >= 0} = {k + h - 1, k + h, ..., 2*k + 2*h - 1}. (3) {a(n) - a(n-1): n >= 1) = {h+k, h+k+1, h+k+2}. (4) {k*b(n)-b(k*n): n >= 0} = {k-2, k-1, ..., 2*k-2} *** Guide to related sequences: h    k     (a(n))     (b(n)) 1    2    A304799    A304800 1    3    A304801    A304802 1    4    A304803    A304804 1    5    A304805    A304806 2    3    A304807    A304808 2    4    A304809    A304810 2    5    A304811    A304812 3    5    A304813    A304814 4    5    A304815    A304816 LINKS Clark Kimberling, Table of n, a(n) for n = 0..10000 C. Kimberling and P. J. C. Moses, Complementary Equations with Advanced Subscripts, J. Int. Seq. 24 (2021) Article 21.3.3. EXAMPLE b(0) = 1, so that a(0) = 2.  Since a(1) = b(1) + b(2), we must have a(1) >= 7, so that b(1) = 3, b(2) = 4, b(3) = 5, b(4) = 6, and a(1) = 7. MATHEMATICA mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); h = 1; k = 2; a = {}; b = {1}; AppendTo[a, mex[Flatten[{a, b}], 1]]; Do[Do[AppendTo[b, mex[Flatten[{a, b}], Last[b]]], {k}];   AppendTo[a, Last[b] + b[[1 + (Length[b] - 1)/k h]]], {500}]; Take[a, 200]  (* A304799 *) Take[b, 200]  (* A304800 *) (* Peter J. C. Moses, May 14 2008 *) CROSSREFS Cf. A304800-A304816. Sequence in context: A130336 A303741 A085303 * A349499 A022886 A047524 Adjacent sequences:  A304796 A304797 A304798 * A304800 A304801 A304802 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 19 2018 EXTENSIONS Comments edited by Clark Kimberling, Jul 07 2019 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 January 26 21:14 EST 2022. Contains 350600 sequences. (Running on oeis4.)