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%I #24 Oct 30 2022 15:06:00
%S 0,1,2,2,1,0,3,4,4,6,8,7,8,2,2,3
%N Decimal expansion of the sum of the alternating series of reciprocals of cubed composite numbers.
%F Equals Sum_{k>=1} (-1)^(k+1)/(A002808(k)^3).
%e Equals 1/(4^3) - 1/(6^3) + 1/(8^3) - 1/(9^3) + ... =
%e 0.0122103446878223...
%o (PARI)
%o composite(n) = {
%o local(c,x);
%o c=1;
%o x=1;
%o while(c <= n,
%o x++;
%o if(!isprime(x),c++);
%o );
%o return(x)
%o }
%o \p 35000
%o sumalt(k=1, (-1)^(k+1)/composite(k)^3)
%o (PARI) upto(n) = my(c=4,s=1,t=0.); while(c<=n, t+=s/c^3; c++; while(isprime(c), c++); s=-s); t
%o upto(n) = my(prev=3,s=1,t=0.); forprime(p=5,n,for(i=prev+1,p-1,t+=s/i^3;s=-s;prev=p));s=-s; t+sum(i=prev+1,n,s=-s;s/i^3) \\ _David A. Corneth_, Apr 29 2017
%Y Cf. A002808, A269229, A275712, A276494.
%K nonn,cons,more
%O 0,3
%A _Terry D. Grant_, Apr 16 2017
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