A394341 Minimum numerators corresponding to the denominators in A395144.

1, 2, 4, 3, 8, 4, 4, 27, 5, 44, 50, 8, 11, 36, 529, 13, 1197, 16, 1378, 11685, 905, 22, 10184, 51488, 119319, 133711, 66553, 268194

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Example

The smallest denominator with a valid fraction is 2 with 1/2 (maximum 2). 1 is the first entry.
The next denominator is 3 with 1/3 and 2/3 = 1/2 + 1/6 (maximum 6 > 2). Thus, 2 is the next entry as it generates the largest denominator.
The next denominator is 4 with 1/4, 2/4 = 1/2, and 3/4 = 1/2 + 1/4 (maximum 4 < 6). No terms will be added here.
The next denominator is 5 with 1/5, 2/5 = 1/3 + 1/15, 3/5 = 1/2 + 1/10, and 4/5 = 1/2 + 1/4 + 1/20 (maximum 20 > 6). Thus, 4 is the next entry as it generates the largest denominator.

Prog

(Julia)
function a(k)
    global_max_num, global_max_den = 0, 0
    i = 0
    den = 1
    while i < k
        den += 1
        local_max_num, local_max_den = 0, 0
        for num in 1:den-1
            frac = num // den
            while numerator(frac) != 1
                frac -= 1 // big(denominator(frac) ÷ numerator(frac) + 1)
            end
            if denominator(frac) > local_max_den
                local_max_num, local_max_den = num, denominator(frac)
            end
        end
        if local_max_den > global_max_den
            global_max_num, global_max_den = local_max_num, local_max_den
            i += 1
        end
    end
    return global_max_num
end

Crossrefs

Cf. A395144 (denominators).

Sequence in context: A347288 A324213 A052131 * A329486 A051145 A288966

Adjacent sequences: A394338 A394339 A394340 * A394342 A394343 A394344

Keyword

frac,nonn,more

Author

Hoang Nguyen, Apr 21 2026

Extensions

a(26)-a(28) from Martin Fuller, May 30 2026

Status

approved