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A230850 A054541 and A000012 interleaved.

%I A230850 #29 Oct 31 2023 07:01:00
%S A230850 2,1,1,1,2,1,2,1,4,1,2,1,4,1,2,1,4,1,6,1,2,1,6,1,4,1,2,1,4,1,6,1,6,1,
%T A230850 2,1,6,1,4,1,2,1,6,1,4,1,6,1,8,1,4,1,2,1,4,1,2,1,4,1,14,1,4,1,6,1,2,1,
%U A230850 10,1,2,1,6,1,6,1,4,1,6,1,6,1,2,1,10,1,2,1
%N A230850 A054541 and A000012 interleaved.
%C A230850 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.
%C A230850 a(2n-1) is the length of the n-th horizontal edge in the staircase.
%C A230850 a(2n) is the length of the n-th vertical edge in the staircase.
%C A230850 For another version see A230849.
%H A230850 Antti Karttunen, <a href="/A230850/b230850.txt">Table of n, a(n) for n = 1..10000</a>
%F A230850 a(1) = 2; for n > 1, a(n) = A230849(n). - _Antti Karttunen_, Dec 23 2018
%e A230850 Illustration of initial terms, n = 1..22:
%e A230850 .
%e A230850 1                                                              _ _|
%e A230850 1                                                  _ _ _ _ _ _|
%e A230850 1                                          _ _ _ _|
%e A230850 1                                      _ _|
%e A230850 1                              _ _ _ _|
%e A230850 1                          _ _|
%e A230850 1                  _ _ _ _|
%e A230850 1              _ _|
%e A230850 1          _ _|
%e A230850 1        _|
%e A230850 1    _ _|
%e A230850 .
%e A230850 .      2 1   2   2       4   2       4   2       4           6   2
%e A230850 .
%e A230850 Drawing vertical line segments below the staircase (as shown below) we have that the number of cells in the vertical bars gives 0 together A000720.
%e A230850 Drawing horizontal line segments above the staircase we have that the number of cells in the k-th horizontal bar is A000040(k).
%e A230850 .    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A230850 31  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e A230850 29  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e A230850 23  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | |
%e A230850 19  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | |
%e A230850 17  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | |
%e A230850 13  |_ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | |
%e A230850 11  |_ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | |
%e A230850 7   |_ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | |
%e A230850 5   |_ _ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | | | |
%e A230850 3   |_ _ _| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
%e A230850 2   |_ _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|
%e A230850 .
%e A230850 .    0 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
%e A230850 .
%t A230850 Riffle[Join[{2},Differences[Prime[Range[100]]]],1] (* _Paolo Xausa_, Oct 31 2023 *)
%o A230850 (PARI) A230850(n) = if(1==n,2,if((n%2),prime((n+1)/2)-prime(((n+1)/2)-1),1)); \\ _Antti Karttunen_, Dec 23 2018
%Y A230850 Cf. A000012, A000040, A000720, A001223, A007504, A046992, A054541, A141042, A152535, A182986, A230849.
%K A230850 nonn
%O A230850 1,1
%A A230850 _Omar E. Pol_, Oct 31 2013