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A162938 A 2-based alternate sum over the numbers from 0 to the n-th nonprime.

%I A162938 #7 Mar 02 2019 23:21:56
%S A162938 2,5,8,11,14,25,17,20,23,40,26,29,32,55,35,38,65,41,70,44,47,50,85,53,
%T A162938 90,56,59,100,62,65,68,115,71,74,125,77,130,80,83,140,86,145,89,92,95,
%U A162938 160,98,165,101,104,175,107,110,113,190,116,195,119,122,205,125,128,215
%N A162938 A 2-based alternate sum over the numbers from 0 to the n-th nonprime.
%C A162938 Define a 2-based sum S(n) = Sum_{i=0..n} (2 - (-1)^i*i) = 2*n - (-1)^n*A152832(n).
%C A162938 a(n) is this sum evaluated at A141468(n).
%F A162938 a(n) = Sum_{x=0..n-th nonprime} (2 - x*(-1)^x). - _Juri-Stepan Gerasimov_, Jul 28 2009
%e A162938 a(1) = 2 - 0*(-1)^0 = 2.
%e A162938 a(2) = 2 - 0*(-1)^0 + 2 - 1*(-1)^1 = 2 + 3 = 5.
%e A162938 a(3) = 2 - 0*(-1)^0 + 2 - 1*(-1)^1 + 2 - 2*(-1)^2 + 2 - 3*(-1)^3 + 2 - 4*(-1)^4 = 2 + 3 + 0 + 5 - 2 = 8.
%p A162938 A152832 := proc(n) option remember; if n = 0 then -2; else n-procname(n-1) ; fi; end:
%p A162938 A141468 := proc(n) option remember ; local a; if n <=2 then n-1; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a); fi; od: fi; end:
%p A162938 A162938 := proc(n) local npr; npr := A141468(n) ; 2*npr-(-1)^npr*A152832(npr) ; end:
%p A162938 seq(A162938(n),n=1..100) ; # _R. J. Mathar_, Jul 21 2009
%Y A162938 Cf. A141468.
%K A162938 nonn
%O A162938 1,1
%A A162938 _Juri-Stepan Gerasimov_, Jul 18 2009
%E A162938 Definition edited by _R. J. Mathar_, Jul 21 2009