A323725 a(n) is the last (and thus largest) denominator of an Egyptian fraction representing n, where each consecutive denominator is as small as possible.

1, 6, 57960, 36802906522516375115639735990520502954652700

Offset

1,2

Comments

Values grow extremely quickly, a(5) has 142548 decimal digits.

The denominators for n = 3 are given in A140335.

The denominators for n = 4 are given in A281873.

The number of terms in the representation of n is A306349(n).

Links

Table of n, a(n) for n=1..4.

Wikipedia, Egyptian fraction

Index entries for sequences related to Egyptian fractions

Example

a(3) = 57960 because (1/1) + (1/2) + (1/3) + (1/4) + (1/5) + (1/6) + (1/7) + (1/8)  + (1/9) + (1/10) + (1/15) + (1/230) + (1/57960) = 3 and the final and greatest denominator is 57960. (Sequence A140335 has the full list of denominators.)

Prog

(PARI) a(n)={my(s=n, k=1); while(s>1/k, s-=1/k; k++); while(s!=0, k=ceil(1/s); s-=1/k); k} \\ Andrew Howroyd, Sep 01 2019
(Python)
from sympy import egyptian_fraction
def A323725(n): return egyptian_fraction(n)[-1] # Pontus von Brömssen, Aug 03 2020

Crossrefs

A140335 and A281873 are the denominatorial sequences for 3 and 4, respectively.

Cf. A306349.

Sequence in context: A289391 A295817 A118859 * A259162 A076913 A101450

Adjacent sequences: A323722 A323723 A323724 * A323726 A323727 A323728

Keyword

nonn

Author

AJ Tatum, Aug 31 2019

Status

approved