A004280 - OEIS

A004280

2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes).

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

Also the mutual-visibility number of the n-crown graph. - Eric W. Weisstein, Dec 31 2025

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).

Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 528.

H. B. Meyer, Eratosthenes' sieve

Eric Weisstein's World of Mathematics, Crown Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Index entries for sequences generated by sieves

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