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 A004280 2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes). 21
 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 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 G.f.: x(1+x^3)/(1-x)^2; a(n) = 2n - 3 + C(1, n-1) + C(0, n-1). - Paul Barry, Mar 05 2007 a(n) = 2*n - 3 + floor(2/n). - Wesley Ivan Hurt, May 23 2013 MAPLE 1, 2, seq(2*n-1, n=2..66); # Emeric Deutsch, May 13 2007 MATHEMATICA Union[ Join[ 2Range[65] - 1, {2}]] (* Robert G. Wilson v *) PROG (PARI) a(n)=2*n + 2\n - 3 \\ Charles R Greathouse IV, Nov 01 2011 CROSSREFS Cf. A002858. Sequence in context: A186330 A153809 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

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Last modified October 17 00:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)