A304286 Sequence gives the denominators, in increasing values, of Egyptian fractions whose sum has the concatenation of these denominators as decimal part. Case a(1) = 4.

4, 5, 316, 617610, 803725588973, 456253083482572713037551, 9436780443304881627624731251391047815103579902912

Offset

1,1

Comments

There are only three possible sequences of this kind: one starting from 3 (A302932), another from 4 (this sequence) and another from 10 (A302933).

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 4: 1/4 = 0.25. At the beginning we have 2 instead of 4 as first decimal digit but the second term will fix it.
In fact the next integer is 5 and 1/4 + 1/5 = 0.45 and so on.
The sum is 0.4 5 316 617610 803725588973 ...

Maple

P:=proc(q) local a, b, d, n; a:=1/4; 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.

Sequence in context: A042181 A368531 A042717 * A134463 A298938 A309071

Adjacent sequences: A304283 A304284 A304285 * A304287 A304288 A304289

Keyword

nonn,base

Author

Paolo P. Lava, Jun 06 2018

Extensions

a(5)-a(7) from Giovanni Resta, Jun 06 2018

Status

approved