OFFSET
0,1
COMMENTS
It appears that fractions of this kind exist only for a(0) equal to 3 (A320306), 10 (A320307), 13 (this sequence) and 38 (A320309).
Next term has 163 digits. - Giovanni Resta, Oct 11 2018
EXAMPLE
1/13 = 0.07692...
At the beginning instead of 13 we have 07 as first decimal digits. Adding the second term this is fixed.
1/13 + 13/(247 - 13) = 0.13247863...
1/13 + 13/(247 - 13) + 247/(890970451 - 247) = 0.13247890970451376...
The sum is 0.13 247 890970451 540818819108243685091145 ...
MAPLE
P:=proc(q, h) local a, b, d, n, t, x; x:=h+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-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(10^20, 13);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Oct 11 2018
EXTENSIONS
a(3)-a(5) from Giovanni Resta, Oct 11 2018
STATUS
approved