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A305666 Denominators of the fraction Sum_{n>=0} {a(n)/a(n+1)} = a(0)/a(1) + a(1)/a(2) + a(2)/a(3) + ... such that the sum has the concatenation of these denominators as decimal part. Case a(0) = 1 and a(1) = 10. 25
1, 10, 3162, 9048102540, 9979213683484174723652691445 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
It appears that there are only three sequences of this kind, with a(1) = 3 (A305664), a(1) = 4 (A305665) and a(1) = 10 (this sequence).
a(5) has 73 digits. - Giovanni Resta, Jun 08 2018
LINKS
EXAMPLE
1/10 = 0.1000...
1/10 + 10/3162 = 0.103162555...
1/10 + 10/3162 + 3162/9048102540 = 0.1031629048102540988...
The sum is 0.10 3162 9048102540 ...
MAPLE
P:=proc(q, h) local a, b, d, n, t, x; x:=1; a:=1/h; b:=ilog10(h)+1;
d:=h; print(d); t:=1/a; for n from x to q do
if trunc(evalf(a+t/n, 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:=n; x:=n+1; print(n); fi; od; end: P(10^20, 10);
CROSSREFS
Sequence in context: A208185 A123377 A061543 * A320307 A225764 A243008
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jun 08 2018
EXTENSIONS
a(3)-a(4) from Giovanni Resta, Jun 08 2018
a(0)=1 inserted. - R. J. Mathar, Jun 19 2021
STATUS
approved

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Last modified February 26 10:27 EST 2024. Contains 370346 sequences. (Running on oeis4.)