A097330 In the sequence of prime numbers replace each term p with floor(p/2) and ceiling(p/2).

1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 14, 15, 15, 16, 18, 19, 20, 21, 21, 22, 23, 24, 26, 27, 29, 30, 30, 31, 33, 34, 35, 36, 36, 37, 39, 40, 41, 42, 44, 45, 48, 49, 50, 51, 51, 52, 53, 54, 54, 55, 56, 57, 63, 64, 65, 66, 68, 69, 69, 70, 74, 75, 75, 76, 78, 79

Offset: 1

Author

Reinhard Zumkeller, Sep 17 2004

Keywords

• nonn

Comments

a(2*n-1) + a(2*n) = A000040(n);

a(2*n) + a(2*n+1) = A024675(n-1) for n > 1;

a(2*n+1) = A005097(n), a(2*(n+1)) = A006254(n).

This is a subsequence of A180108. - Parthasarathy Nambi, Aug 14 2010

Sum_{n>=1} (-1)^a(n) * log(a(n)) = log(2). - Dimitris Valianatos, Jun 14 2016

Examples

			__ 2; __ 3; __ 5; __ 7; _ 11; _ 13; _ 17; __ 19; ...
1, 1; 1, 2; 2, 3; 3, 4; 5, 6; 6, 7; 8, 9; 9, 10; ...
1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, ....
		

Programs

PARI

a(n)=if(n<3,return(1),return((prime((n+n%2)/2)+1)/2-n%2)); \\ Dimitris Valianatos, Jun 14 2016

Formula

a(n) = 1 if n < 3, otherwise (prime((n + (n mod 2))/2) + 1)/2 - n mod 2.