This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A276885 Sums-complement of the Beatty sequence for 1 + phi. 3
 1, 4, 9, 12, 17, 22, 25, 30, 33, 38, 43, 46, 51, 56, 59, 64, 67, 72, 77, 80, 85, 88, 93, 98, 101, 106, 111, 114, 119, 122, 127, 132, 135, 140, 145, 148, 153, 156, 161, 166, 169, 174, 177, 182, 187, 190, 195, 200, 203, 208, 211, 216, 221, 224, 229, 232, 237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A276871 for a definition of sums-complement and guide to related sequences. This appears to be 1 followed by A089910. - R. J. Mathar, Oct 05 2016 Mathar's conjecture is proved in the paper 'The Frobenius problem for homomorphic embeddings of languages into the integers'. See Example 1 in that paper. - Michel Dekking, Dec 21 2017 LINKS Michel Dekking, The Frobenius problem for homomorphic embeddings of languages into the integers, arXiv:1712.03345 [math.CO], 2017. FORMULA a(n) = 2[(n-1)phi] + n, where phi = (1+sqrt(5))/2 (see Example 1 in the paper 'The Frobenius problem for homomorphic embeddings of languages into the integers'). - Michel Dekking, Dec 21 2017 a(n) = A035336(n-1)+2 for n>1. - Michel Dekking, Dec 21 2017 EXAMPLE The Beatty sequence for 1 + phi is A001950 = (2,5,7,10,13,15,18,20,23,26,...), with difference sequence s = A005614 + 2 = (3,2,3,3,2,3,2,3,3,...). The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,7,8,10,11,13,14,15,16,18,...), with complement (1,4,9,12,17,22,...). MATHEMATICA z = 500; r = 1 + GoldenRatio; b = Table[Floor[k*r], {k, 0, z}]; (* A001950 *) t = Differences[b]; (* 2 + A003849 *) c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}]; u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]]; w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w]; (* A276885 *) CROSSREFS Cf. A001950, A003849, A276871. Sequence in context: A312860 A312861 A301688 * A089910 A312862 A177880 Adjacent sequences:  A276882 A276883 A276884 * A276886 A276887 A276888 KEYWORD nonn,easy AUTHOR Clark Kimberling, Oct 01 2016 EXTENSIONS Name edited and example corrected by Michel Dekking, Oct 30 2016 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 6 08:53 EST 2019. Contains 329788 sequences. (Running on oeis4.)