Beatty · 86 sequences
The sequences of the family “Beatty”, by A-number, with the share of their decomposable terms in the level class (k > L).
- primes · 1717
- polynomial · 1232
- quadratic form · 430
- prime values · 423
- residue class · 357
- digit rule · 306
- multiplicative · 199
- Beatty · 86
- divisor functions · 58
- binary rule · 48
- self-referential · 35
- complement · 23
- powers · 22
- summatory · 21
- arithmetic progression · 10
- smooth · 10
- forced divisor · 9
- sieve · 8
- block · 5
- base case · 1
| A-number | Name | Level |
|---|---|---|
| A000062 | A Beatty sequence: a(n) = floor(n/(e-2)) | 11.2 % |
| A000201 | Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622 | 12.2 % |
| A001950 | Upper Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi^2), where phi = (1+sqrt(5))/2 | 15.4 % |
| A001951 | A Beatty sequence: a(n) = floor(n*sqrt(2)) | 11.4 % |
| A001952 | A Beatty sequence: a(n) = floor(n*(2 + sqrt(2))) | 17.2 % |
| A001953 | a(n) = floor((n + 1/2) * sqrt(2)) | 11.3 % |
| A001954 | a(n) = floor((n+1/2)*(2+sqrt(2))); winning positions in the 2-Wythoff game | 17.3 % |
| A001961 | A Beatty sequence: floor(n * (sqrt(5) - 1)) | 10.6 % |
| A003151 | Beatty sequence for 1+sqrt(2); a(n) = floor(n*(1+sqrt(2))) | 14.9 % |
| A003152 | A Beatty sequence: a(n) = floor(n*(1+1/sqrt(2))) | 12.5 % |
| A003231 | a(n) = floor(n*(sqrt(5)+5)/2) | 17.7 % |
| A003511 | A Beatty sequence: floor( n * (1 + sqrt(3))/2 ) | 11.3 % |
| A003512 | A Beatty sequence: floor(n*(sqrt(3) + 2)) | 18.0 % |
| A003622 | The Wythoff compound sequence AA: a(n) = floor(n*phi^2) - 1, where phi = (1+sqrt(5))/2 | 15.5 % |
| A003623 | Wythoff AB-numbers: floor(floor(n*phi^2)*phi), where phi = (1+sqrt(5))/2 | 18.6 % |
| A004919 | a(n) = floor(n*phi^4), where phi is the golden ratio, A001622 | 22.3 % |
| A004920 | a(n) = floor(n*phi^5), where phi is the golden ratio, A001622 | 25.8 % |
| A004921 | a(n) = floor(n*phi^6), phi = golden ratio, A001622 | 29.2 % |
| A004922 | a(n) = floor(n*phi^7), where phi is the golden ratio, A001622 | 32.4 % |
| A004976 | a(n) = floor(n*phi^3), where phi=(1+sqrt(5))/2 | 18.9 % |
| A007064 | Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2 | 15.4 % |
| A007066 | a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2 | 15.5 % |
| A022342 | Integers with "even" Zeckendorf expansions (do not end with ... + F_2 = ... + 1) (the Fibonacci-even numbers); also, apart from first term, a(n) = Fibonacci successor to n-1 | 12.3 % |
| A022838 | Beatty sequence for sqrt(3); complement of A054406 | 12.7 % |
| A022839 | Beatty sequence for sqrt(5) | 14.4 % |
| A022840 | Beatty sequence for sqrt(6) | 15.1 % |
| A022841 | Beatty sequence for sqrt(7) | 15.6 % |
| A022842 | Beatty sequence for sqrt(8) | 16.0 % |
| A022843 | Beatty sequence for e: a(n) = floor(n*e) | 15.7 % |
| A022844 | a(n) = floor(n*Pi) | 16.8 % |
| A022846 | Nearest integer to n*sqrt(2) | 11.3 % |
| A022847 | Integer nearest n*sqrt(3) | 12.7 % |
| A022848 | Integer nearest nx, where x = sqrt(5) | 14.5 % |
| A026351 | a(n) = floor(n*phi) + 1, where phi = (1+sqrt(5))/2 | 12.1 % |
| A035336 | a(n) = 2*floor(n*phi) + n - 1, where phi = (1+sqrt(5))/2 | 18.6 % |
| A037085 | Beatty sequence for Pi^2 | 24.8 % |
| A037086 | Beatty sequence for sqrt(Pi) | 12.8 % |
| A037087 | Beatty sequence for e^(1/e) | 11.4 % |
| A038130 | Beatty sequence for 2*Pi | 21.9 % |
| A038152 | Beatty sequence for e^Pi | 30.7 % |
| A038153 | Beatty sequence for Pi^e | 30.5 % |
| A054385 | Beatty sequence for e/(e-1); complement of A022843 | 12.1 % |
| A054386 | Beatty sequence for Pi/(Pi-1); complement of A022844 | 11.6 % |
| A054965 | Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal number | 14.0 % |
| A059531 | Beatty sequence for 1 + 1/Pi | 11.0 % |
| A059532 | Beatty sequence for 1 + Pi | 18.4 % |
| A059535 | Beatty sequence for Pi^2/6, or zeta(2) | 12.4 % |
| A059536 | Beatty sequence for zeta(2)/(zeta(2)-1) | 15.2 % |
| A059537 | Beatty sequence for zeta(3) | 10.5 % |
| A059538 | Beatty sequence for zeta(3)/(zeta(3)-1) | 21.3 % |
| A059539 | Beatty sequence for 3^(1/3) | 11.5 % |
| A059540 | Beatty sequence for 3^(1/3)/(3^(1/3)-1) | 17.1 % |
| A059541 | Beatty sequence for 1 + log(2) | 12.4 % |
| A059542 | Beatty sequence for 1 + 1/log(2) | 15.0 % |
| A059543 | Beatty sequence for log(3) | 10.0 % |
| A059544 | Beatty sequence for log(3)/(log(3)-1) | 25.7 % |
| A059545 | Beatty sequence for log(10) | 14.7 % |
| A059546 | Beatty sequence for log(10)/(log(10)-1) | 12.9 % |
| A059547 | Beatty sequence for 1 + 1/log(3) | 13.4 % |
| A059548 | Beatty sequence for 1 + log(3) | 14.0 % |
| A059549 | Beatty sequence for 1 + 1/log(10) | 11.6 % |
| A059550 | Beatty sequence for 1 + log(10) | 17.2 % |
| A059551 | Beatty sequence for Gamma(1/3) | 15.6 % |
| A059552 | Beatty sequence for Gamma(1/3)/(Gamma(1/3)-1) | 12.1 % |
| A059553 | Beatty sequence for Gamma(2/3) | 11.0 % |
| A059554 | Beatty sequence for Gamma(2/3)/(Gamma(2/3)-1) | 18.1 % |
| A059556 | Beatty sequence for 1 + 1/gamma | 15.8 % |
| A059557 | Beatty sequence for 1 + gamma^2, (gamma is the Euler-Mascheroni constant A001620) | 11.1 % |
| A059559 | Beatty sequence for 1 + log(1/gamma), (gamma is the Euler-Mascheroni constant A001620) | 11.9 % |
| A059560 | Beatty sequence for 1 - 1/log(gamma) | 15.9 % |
| A059562 | Beatty sequence for log(Pi)/(log(Pi)-1) | 23.3 % |
| A059563 | Beatty sequence for e + 1/e | 16.8 % |
| A059564 | Beatty sequence for (e^2 + 1)/(e^2 - e + 1) | 11.8 % |
| A059566 | Beatty sequence for e^gamma/(e^gamma-1) | 14.5 % |
| A059567 | Beatty sequence for 1 - log(log(2)) | 11.3 % |
| A059568 | Beatty sequence for 1 - 1/log(log(2)) | 17.9 % |
| A066343 | Beatty sequence for log_2(10) | 17.1 % |
| A066344 | Beatty sequence for log_5(10) | 11.4 % |
| A087057 | Smallest number whose square is larger than 2*n^2 | 11.3 % |
| A098005 | Beatty sequence for 1/(3 - e): a(n) = floor(n/(3-e)) | 17.5 % |
| A108598 | a(n) = floor(n*((5+sqrt(5))/4)) | 13.0 % |
| A121283 | a(n) = floor(n*Pi*e) | 23.7 % |
| A182760 | Beatty sequence for (3 + 5^(-1/2))/2 | 12.6 % |
| A184618 | a(n) = floor(n*r + h), where r=sqrt(2) and h=1/3; complement of A184619 | 11.3 % |
| A184774 | Primes of the form floor(k*sqrt(2)) | 25.8 % |
| A279607 | Beatty sequence for e/2; i.e., a(n) = floor(n*e/2) | 11.2 % |