VOOZH about

URL: https://oeis.org/A323725

⇱ A323725 - OEIS

login
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.
2
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).
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))[-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 A101439
KEYWORD
nonn
AUTHOR
AJ Tatum, Aug 31 2019
STATUS
approved