A304287 Sequence gives the denominators, in increasing values from the second term on, of Egyptian fractions whose sum has the concatenation of these denominators as decimal part. Case a(1) = 5.

5, 3, 524, 414362, 964900433080, 568112044247363806135385, 532690079132413282557643073103806291708903760733

Offset

1,1

Comments

Next term has 97 digits. - Giovanni Resta, Jun 06 2018

Links

Table of n, a(n) for n=1..7.

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 5: 1/5 = 0.2. At the beginning we have 2 instead of 5 as first decimal digit but the second term will fix it.
In fact the next integer is 3 and 1/5 + 1/3 = 0.5333... and so on.
The sum is 0.5 3 524 414362 964900433080 ...

Maple

P:=proc(q) local a, b, d, n; a:=1/5; b:=ilog10(1/a)+1; d:=1/a; 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. A302932, A302933, A303388, A304285, A304286.

Sequence in context: A002208 A100653 A105318 * A121021 A237518 A274649

Adjacent sequences: A304284 A304285 A304286 * A304288 A304289 A304290

Keyword

nonn,base

Author

Paolo P. Lava, Jun 06 2018

Extensions

a(4)-a(7) from Giovanni Resta, Jun 06 2018

Status

approved