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A285308
Decimal expansion of the sum of the alternating series of reciprocals of cubed composite numbers.
0
0, 1, 2, 2, 1, 0, 3, 4, 4, 6, 8, 7, 8, 2, 2, 3
OFFSET
0,3
FORMULA
Equals Sum_{k>=1} (-1)^(k+1)/(A002808(k)^3).
EXAMPLE
Equals 1/(4^3) - 1/(6^3) + 1/(8^3) - 1/(9^3) + ... =
0.0122103446878223...
PROG
(PARI)
composite(n) = {
local(c, x);
c=1;
x=1;
while(c <= n,
x++;
if(!isprime(x), c++);
);
return(x)
}
\p 35000
sumalt(k=1, (-1)^(k+1)/composite(k)^3)
(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
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
CROSSREFS
KEYWORD
nonn,cons,more
AUTHOR
Terry D. Grant, Apr 16 2017
STATUS
approved