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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 (list; constant; graph; refs; listen; history; text; internal format)
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, 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

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

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Last modified January 18 15:35 EST 2021. Contains 340254 sequences. (Running on oeis4.)