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%I #14 Sep 05 2016 17:26:08
%S 0,0,0,1,2,3,4,5,8,9,12,11,14,17,20,23,24,23,24,29,36,37,38,35,36,41,
%T 48,53,56,53,50,51,56,63,76,75,74,63,74,77,94,89,90,79,90,91,112,103,
%U 106,87,108,117,140
%N a(n+3) = A008578(n+1) -a(n), a(0) = a(1) = a(2) = 0.
%C A008578 gives the noncomposite numbers, the prime numbers at the beginning of the 20th century which included 1.
%C a(2n) = 0, 0, 2, 4, 8, 12, 14, 20, 24, 24, ... always even?
%C a(2n+3) = 1, 3, 5, 9, 11, 17, 23, 23, 29, ... always odd?
%C First differences: 0, 0, 1, 1, 1, 1, 1, 3, 1, 3, -1, 3, 3, 3, 3, 1, -1, 1, 5, 7, ... .
%e a(3) = 1-0 = 1, a(4) = 2-0 = 2, a(5) = 3-0 = 3, a(6) = 5-1 = 4, a(6) = 7-2 = 5, ... .
%t RecurrenceTable[{a[n + 3] == If[n == 0, 1, Prime[n]] - a[n], a[0] == 0, a[1] == 0, a[2] == 0}, a, {n, 0, 52}] (* _Michael De Vlieger_, Aug 08 2016 *)
%Y Cf. A000040, A008578, A113405, A274817.
%K nonn
%O 0,5
%A _Paul Curtz_, Aug 08 2016
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