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A004280
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2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes).
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13
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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; internal format)
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OFFSET
| 0,2
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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 (deutsch(AT)duke.poly.edu), 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.
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REFERENCES
| F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 256.
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LINKS
| H. B. Meyer, Eratosthenes' sieve
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
Index entries for sequences generated by sieves
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FORMULA
| G.f.: (1+x^3)/(1-x)^2; a(n)=2n-1+C(1,n)+C(0,n); - Paul Barry (pbarry(AT)wit.ie), Mar 05 2007
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MAPLE
| 1, 2, seq(2*n-1, n=2..66); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2007
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MATHEMATICA
| Union[ Join[ 2Range[65] - 1, {2}]] (* Robert G. Wilson v *)
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PROG
| (PARI) a(n)=n+if(n>3, n-3) \\ Charles R Greathouse IV, Nov 01 2011
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CROSSREFS
| Cf. A002858.
Sequence in context: A186330 A153809 A004274 * A053224 A091377 A005357
Adjacent sequences: A004277 A004278 A004279 * A004281 A004282 A004283
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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