A305662 Denominators a(n) of the fractions Sum_{n>=1} {n/a(n)} = 1/a(1) + 2/a(2) + 3/a(3) + ... such that the sum has the concatenation of these denominators as decimal part. Case a(1) = 14.

14, 28, 619829, 64119408562, 89683259163592378754652, 97322840981260080521305808534009505107316888799

Offset

1,1

Comments

It appears that fractions of this kind exist only for a(1) equal to 3 (A304288), 10 (A304289), 11 (A305661), 14 (this sequence), and 31 (A305663).

a(7) has 94 digits. - Giovanni Resta, Jun 08 2018

Links

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

Example

1/14 = 0.07142... At the beginning instead of 14 we have 07 as first decimal digits. Adding the second term this is fixed.
1/14 + 2/28 = 0.14285771...
1/14 + 2/28 + 3/619829 = 0.1428619829017...
The sum is 0.14 28 619829...

Maple

P:=proc(q, h) local a, b, d, n, t; a:=1/h; b:=ilog10(h)+1; d:=h; print(d);
t:=2; for n from 1 to q do if trunc(evalf(a+t/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+t/n; t:=t+1; print(n);  fi; od; end: P(10^20, 14);

Crossrefs

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305663, A305664, A305665, A305666.

Sequence in context: A212890 A019552 A325728 * A174070 A045527 A353197

Adjacent sequences: A305659 A305660 A305661 * A305663 A305664 A305665

Keyword

nonn,base

Author

Paolo P. Lava, Jun 08 2018

Extensions

a(4)-a(6) from Giovanni Resta, Jun 08 2018

Status

approved