login
A070987
Number of terms in simple continued fraction for sum(k=1,n,1/k^4).
1
1, 2, 8, 8, 9, 12, 22, 23, 27, 29, 33, 33, 49, 39, 48, 52, 58, 62, 65, 68, 73, 67, 75, 72, 80, 83, 87, 89, 100, 91, 93, 109, 113, 112, 101, 105, 107, 118, 123, 131, 118, 120, 123, 141, 151, 148, 157, 165, 157, 170, 180, 158, 187, 181, 181, 195, 187, 181, 194, 188
OFFSET
1,2
COMMENTS
sum(k>=1,1/k^4)=zeta(4)=Pi^4/90
LINKS
FORMULA
lim n ->infinity a(n)/n=C=3, 3....
EXAMPLE
The simple continued fraction for sum(k=1,10,1/k^4) is [1, 12, 5, 3, 1, 2, 10, 12, 1, 2, 4, 2, 2, 2, 1, 7, 11, 1, 1, 2, 5, 2, 2, 4, 3, 1, 1, 1, 2] which contains 29 terms, hence a(10)=29.
MATHEMATICA
Length[ContinuedFraction[#]]&/@Accumulate[1/Range[60]^4] (* Harvey P. Dale, Dec 20 2012 *)
PROG
(PARI) for(n=1, 100, print1(length(contfrac(sum(i=1, n, 1/i^4))), ", "))
CROSSREFS
Cf. A055573.
Sequence in context: A193639 A154481 A092280 * A168286 A079458 A281914
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 18 2002
STATUS
approved