

A302932


Sequence gives the denominators, in increasing values, of Egyptian fractions such that their sum has the concatenation of these denominators as decimal part. Case a(1) = 3.


22




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 bfile).  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

Cf. A302933, A303388, A304286.
Sequence in context: A136723 A202649 A347611 * A143387 A228452 A269458
Adjacent sequences: A302929 A302930 A302931 * A302933 A302934 A302935


KEYWORD

nonn,base


AUTHOR

Paolo P. Lava, Apr 16 2018


EXTENSIONS

a(4)a(7) from Giovanni Resta, Apr 16 2018


STATUS

approved



