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A257839 Smallest possible x such that 4/n = 1/x + 1/y + 1/z with 0 < x < y < z all integers, or 0 if there is no such solution. Corresponding y and z values are in A257840 and A257841. 5
0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 14, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 20, 19, 19, 20, 20, 20, 20, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Otherwise said, x-value of the lexicographically first solution (x,y,z) to the given equation.
See A073101 for more details about these sequences related to the Erdős-Straus conjecture.
This differs from A075245 starting with a(89)=23 vs A075245(89)=24, respective solutions being 1/23 + 1/690 + 1/61410 = 1/24 + 1/306 + 1/108936 = 4/89.
LINKS
FORMULA
Conjecture: a(n) = floor(n/4) + d with d = 1 for all n > 2 except some n = 24k + 1 (k = 2, 3, 7, 8, 10, 13, 15, 17, 18, 23, 25, 28, 30, 32, 33, 37, 40, 43, ...) where d = 2. - M. F. Hasler, Jul 03 2022
PROG
(PARI) apply( {A257839(n, t)=for(x=n\4+1, 3*n\4, for(y=max(1\t=4/n-1/x, x)+1, ceil(2/t)-1, numerator(t-1/y)==1 && return(x)))}, [1..99]) \\ improved by M. F. Hasler, Jul 03 2022
CROSSREFS
Sequence in context: A008621 A144075 A128929 * A075245 A367329 A328301
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 16 2015
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)