The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320335 Numerators of the fractions a(0)/(a(1) - a(0)), a(1)/(a(2) - a(1)), a(2)/(a(3) - a(2)), ... such that the sum Sum_{n>=1} a(n-1)/(a(n) - a(n-1)) has the concatenation of these numerators, starting from a(1), as decimal part. Case a(0) = 1, a(1) = 4. 11
1, 4, 41, 89814, 98285430640360, 22352043009017562549812304739324022523 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
It appears that fractions of this kind with a(0)=1 exist only for a(1) equal to 4 (this sequence) and 13 (A320336).
Next term has 98 digits. - Giovanni Resta, Oct 11 2018
LINKS
EXAMPLE
1/(4-1) = 0.3333...
At the beginning instead of 4 we have 3 as first decimal digit. Adding the second term this is fixed.
1/(4-1) + 4/(41 - 4) = 0.441441...
1/(4-1) + 4/(41 - 4) + 41/(89814 - 41) = 0.44189814891 ...
The sum is 0.4 41 89814 98285430640360 ...
MAPLE
P:=proc(q, h) local a, b, d, t, x, n; x:=1; a:=1/(h-1); b:=ilog10(h-1)+1; d:=h; print(d); t:=h; for n from h+1 to q do if trunc(evalf(a+t/(n-t), 100)*10^(b+ilog10(n)+1))=d*10^(ilog10(n)+1)+n then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+t/(n-t); t:=n; x:=n+1; print(n); fi; od; end: P(10^10, 4);
CROSSREFS
Sequence in context: A333731 A326899 A022500 * A076652 A078288 A349455
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Oct 11 2018
EXTENSIONS
a(4)-a(5) from Giovanni Resta, Oct 11 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 12:15 EDT 2024. Contains 372692 sequences. (Running on oeis4.)