A303388 Sequence gives the denominators, in increasing values, of Egyptian fractions such that their alternating sum has the concatenation of these denominators as decimal part. a(1) = 3.

3, 299, 98957, 118885566690, 7993597110943689863079

Offset

1,1

Comments

Similar to A302932.

a(6) > 10^40. - Giovanni Resta, Apr 23 2018

Links

Table of n, a(n) for n=1..5.

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 299 because 1/3 - 1/299 = 0.32998885.
Next term is 98957 because 1/3 - 1/299 + 1/98957 = 0.3299989571272... and so on.
The alternating sum is 0.3 299 98957 118885566690 ...

Maple

with(numtheory): P:=proc(q) local a, b, d, n, t; a:=1/3; b:=1; d:=3; print(d); t:=1;
for n from 1 to q do if trunc(evalf(a+(-1)^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+(-1)^t/n; t:=t+1; print(n); fi; od; end: P(10^20);

Crossrefs

Cf. A302932, A302933.

Sequence in context: A104821 A282195 A334177 * A328044 A119065 A119069

Adjacent sequences: A303385 A303386 A303387 * A303389 A303390 A303391

Keyword

nonn,base,more

Author

Paolo P. Lava, Apr 23 2018

Extensions

a(4)-a(5) from Giovanni Resta, Apr 23 2018

Status

approved