

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
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OFFSET

0,3


COMMENTS

Using an approach similar to the one described in the Nov 10 2016 comments at A275712 (see the charts in that sequence's Links), I am confident that this constant is 0.01221034468782231413473583117487004398688..., with the next digit probably a 9.  Jon E. Schoenfield, Jan 16 2018


LINKS

Table of n, a(n) for n=0..15.


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, p1, 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

Cf. A002808, A269229, A275712, A276494.
Sequence in context: A285099 A306754 A063250 * A276543 A107424 A155161
Adjacent sequences: A285305 A285306 A285307 * A285309 A285310 A285311


KEYWORD

nonn,cons,more


AUTHOR

Terry D. Grant, Apr 16 2017


STATUS

approved



