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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A004280 2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes). 23
 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of Fibonacci binary words of length n and having no subword 1011. A Fibonacci binary word is a binary word having no 00 subword. Example: a(5) = 9 because of the 13 Fibonacci binary words of length 5 the following do not qualify: 11011, 10110, 10111 and 01011. - Emeric Deutsch, May 13 2007 a(1) = 1; for n > 1, a(n) = least number > a(n-1) which is a unique sum of two earlier terms, not necessarily distinct. - Franklin T. Adams-Watters, Nov 01 2011 REFERENCES F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 256. LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 Borys Kuca, Structures in Additive Sequences, arXiv:1804.09594 [math.NT], 2018. See V(1,2). H. B. Meyer, Eratosthenes' sieve Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA From Paul Barry, Mar 05 2007: (Start) G.f.: x*(1+x^3)/(1-x)^2; a(n) = 2*n - 3 + C(1, n-1) + C(0, n-1). (End) a(n) = 2*n - 3 + floor(2/n). - Wesley Ivan Hurt, May 23 2013 E.g.f.: (1/2)*(6 + 4*x + x^2 - 2*(3 - 2*x)*exp(x)). - G. C. Greubel, Nov 25 2021 MAPLE 1, 2, seq(2*n-1, n=2..70); # Emeric Deutsch, May 13 2007 MATHEMATICA Union[ Join[ 2Range[70] - 1, {2}]] (* Robert G. Wilson v *) PROG (PARI) a(n)=2*n + 2\n - 3 \\ Charles R Greathouse IV, Nov 01 2011 (Sage) [1, 2]+[2*n-3 for n in (3..70)] # G. C. Greubel, Nov 25 2021 CROSSREFS Cf. A002858. Sequence in context: A355330 A338923 A004274 * A053224 A277334 A091377 Adjacent sequences: A004277 A004278 A004279 * A004281 A004282 A004283 KEYWORD easy,nonn AUTHOR EXTENSIONS Offset changed to 1 and formulas updated accordingly (at the suggestion of Michel Marcus) by Charles R Greathouse IV, Sep 03 2013 STATUS approved

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

Last modified December 5 06:35 EST 2022. Contains 358582 sequences. (Running on oeis4.)