OFFSET
1,5
COMMENTS
a(n) is also the length of the n-th edge of a staircase which represents the function pi(x) on the first quadrant of the square grid, see A000720.
a(2n-1) is the length of the n-th horizontal edge in the staircase.
a(2n) is the length of the n-th vertical edge in the staircase.
For another version see A230850.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
EXAMPLE
Illustration of initial terms, n = 1..22:
.
1 _ _|
1 _ _ _ _ _ _|
1 _ _ _ _|
1 _ _|
1 _ _ _ _|
1 _ _|
1 _ _ _ _|
1 _ _|
1 _ _|
1 _|
1 _|
.
. 1 1 2 2 4 2 4 2 4 6 2
.
Drawing vertical line segments below the staircase (as shown below) we have that the number of cells in the vertical bars gives A000720.
Drawing horizontal line segments above the staircase we have that the number of cells in the k-th horizontal bar is A006093(k).
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
30 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
28 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
22 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | |
18 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | |
16 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | |
12 |_ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | |
10 |_ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | |
6 |_ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | |
4 |_ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | | | |
2 |_ _| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|
.
. 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10
.
MATHEMATICA
Riffle[Join[{1}, Differences[Prime[Range[100]]]], 1] (* Paolo Xausa, Oct 31 2023 *)
PROG
(PARI) A230849(n) = if((n%2)&&(n>1), prime((n+1)/2)-prime(((n+1)/2)-1), 1); \\ Antti Karttunen, Dec 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 01 2013
STATUS
approved