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%I #20 May 08 2021 23:37:36
%S 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,
%T 23,24,26,27,29,30,30,31,33,34,35,36,36,37,39,40,41,42,44,45,48,49,50,
%U 51,51,52,53,54,54,55,56,57,63,64,65,66,68,69,69,70,74,75,75,76,78,79
%N In the sequence of prime numbers replace each term p with floor(p/2) and ceiling(p/2).
%C a(2*n-1) + a(2*n) = A000040(n);
%C a(2*n) + a(2*n+1) = A024675(n-1) for n > 1;
%C a(2*n+1) = A005097(n), a(2*(n+1)) = A006254(n).
%C This is a subsequence of A180108. - _Parthasarathy Nambi_, Aug 14 2010
%C Sum_{n>=1} (-1)^a(n) * log(a(n)) = log(2). - _Dimitris Valianatos_, Jun 14 2016
%F a(n) = 1 if n < 3, otherwise (prime((n + (n mod 2))/2) + 1)/2 - n mod 2.
%e __ 2; __ 3; __ 5; __ 7; _ 11; _ 13; _ 17; __ 19; ...
%e 1, 1; 1, 2; 2, 3; 3, 4; 5, 6; 6, 7; 8, 9; 9, 10; ...
%e 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, ....
%o (PARI) a(n)=if(n<3,return(1),return((prime((n+n%2)/2)+1)/2-n%2)); \\ _Dimitris Valianatos_, Jun 14 2016
%K nonn
%O 1,4
%A _Reinhard Zumkeller_, Sep 17 2004
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