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%I #8 Mar 03 2019 01:56:59
%S 1,3,3,4,5,15,6,7,8,24,9,10,11,33,12,13,39,14,42,15,16,17,51,18,54,19,
%T 20,60,21,22,23,69,24,25,75,26,78,27,28,84,29,87,30,31,32,96,33,99,34,
%U 35,105,36,37,38,114,39,117,40,41,123,42,43,129,44,132,45,46,138,47,141
%N An alternating sum of the first n nonprimes.
%C Define an alternating 1-based sum S(n) = (1-0)+(1+1)+(1-2)+...(1-(-1)^n*n) = A064455(n+1).
%C The sequence evaluates this sum for an upper limit of the n-th nonprime A141468(n).
%F a(n) = A064455(A141468(n)+1). - _R. J. Mathar_, Jul 19 2009
%e a(1) = 1 = 1 - (-1)^0*0.
%e a(2) = 3 = 1 - (-1)^0*0 + 1 -(-1)^1*1.
%e a(3) = 3 = 1 - (-1)^0*0 + 1 -(-1)^1*1 + 1 - (-2)^2*2 + 1 - (-1)^3*3 + 1 - (-1)^4*4.
%p A141468 := proc(n) option remember; local a; if n = 1 then 0 ; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end:
%p A064455 := proc(n) if type(n,'even') then 3*n/2; else (n+1)/2 ; fi; end:
%p A162888 := proc(n) A064455(A141468(n)+1) ; end: seq(A162888(n),n=1..100) ; # _R. J. Mathar_, Jul 19 2009
%Y Cf. A064455, A141468.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Jul 16 2009
%E Definition edited by _R. J. Mathar_, Jul 19 2009
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