OFFSET
1,1
COMMENTS
There are only three possible sequences of this kind: one starting from 3 (this sequence), another from 4 (A304286) and another from 10 (A302933).
Next term a(8) has 152 digits (see b-file). - Giovanni Resta, Apr 16 2018
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..8
Eric Weisstein's World of Mathematics, Egyptian fraction
Eric Weisstein's World of Mathematics, Trott constants (similar but with continued fractions)
EXAMPLE
We start from 3 because 1/3 = 0.3333...
Then the next integer is 52 because 1/3 + 1/52 = 0.352564... and so on.
The sum is 0.3 52 58130 684605953 18209086488275508678 ...
MAPLE
P:=proc(q) local a, b, d, n; a:=1/3; b:=1; d:=3; print(d);
for n from 1 to q do if trunc(evalf(a+1/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+1/n; print(n); fi;
od; end: P(10^20);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Apr 16 2018
EXTENSIONS
a(4)-a(7) from Giovanni Resta, Apr 16 2018
STATUS
approved