OFFSET
0,2
COMMENTS
It appears that there are only three sequences of this kind, with a(1) = 3 (A305664), a(1) = 4 (this sequence) and a(1) = 10 (A305666).
a(6) has 110 digits. - Giovanni Resta, Jun 08 2018
EXAMPLE
1/4 = 0.3333...
1/4 + 4/23 = 0.3407043...
1/4 + 4/23 + 23/937574= 0.34076600381136...
The sum is 0.3 407 6600381 ...
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, 4);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jun 08 2018
EXTENSIONS
a(4)-a(5) from Giovanni Resta, Jun 08 2018
a(0)=1 inserted. - R. J. Mathar, Jun 19 2021
STATUS
approved