A304285 Sequence gives the odd denominators, in increasing values, of Egyptian fractions whose sum has the concatenation of these denominators as decimal part. Case a(1) = 3.

3, 361, 33377, 18729544521131, 9213597883194972217398739, 1057864824471295887547891513136603404869521279141573

Offset

1,1

Comments

Similar to A302932 but here only odd denominators are used.

Next term has 103 digits. - Giovanni Resta, Jun 06 2018

Links

Table of n, a(n) for n=1..6.

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 odd integer is 361 because 1/3 + 1/361 = 0.3361034... and so on.
The sum is 0.3 361 33377 18729544521131 ...

Maple

P:=proc(q) local a, b, d, n; a:=1/3; b:=1; d:=1/a; print(d);
for n from 1 by 2 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, A304286.

Sequence in context: A355753 A324402 A324427 * A324269 A173648 A110717

Adjacent sequences: A304282 A304283 A304284 * A304286 A304287 A304288

Keyword

nonn,base

Author

Paolo P. Lava, Jun 06 2018

Extensions

a(4)-a(6) from Giovanni Resta, Jun 06 2018

Status

approved