A323725 - OEIS

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

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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