|
|
A083479
|
|
The natural numbers with all terms of A033638 inserted.
|
|
8
|
|
|
0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 56, 57, 57
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Row n of A049597 has a(n+1) nonzero values.
When considering the set of nested parabolas defined by -(x^2) + p*x for integer values of p, a(n) tells us how many parabolas are intersected by the line from (1,n) to (n,n). - Gregory R. Bryant, Apr 01 2013
Number of distinct perimeters for polyominoes with n square cells. - Wesley Prosser, Sep 06 2017
|
|
LINKS
|
|
|
FORMULA
|
(End)
|
|
EXAMPLE
|
There are three 1's, one from the natural numbers and two from A033638.
When viewed as an array the sequence begins:
0
1
1 1
2 2
3 3 4
5 5 6
7 7 8 9
10 10 11 12
13 13 14 15 16
17 17 18 19 20
21 21 22 23 24 25
26 26 27 28 29 30
...
|
|
MATHEMATICA
|
Table[(n + 2) - Ceiling@ Sqrt[4 n] - 2 Boole[n == 0], {n, 0, 73}] (* Michael De Vlieger, Sep 05 2017 *)
|
|
PROG
|
(Haskell)
a083479 n = a083479_list !! n
a083479_list = m [0..] a033638_list where
m xs'@(x:xs) ys'@(y:ys) | x <= y = x : m xs ys'
| otherwise = y : m xs' ys
(Maxima)
(Python)
from math import isqrt
(Magma) [n eq 0 select 0 else (n+2)-Ceiling(Sqrt(4*n)): n in [0..100]]; // G. C. Greubel, Feb 17 2024
(SageMath) [(n+2)-ceil(sqrt(4*n)) -2*int(n==0) for n in range(101)] # G. C. Greubel, Feb 17 2024
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,tabf
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|