experimental-projects/oeis-research/Lorenzo Sauras Altuzarra/Inverse tetrahedral/prog.sf

#!/usr/bin/ruby

local Num!PREC = 1024

func inverse_tetrahedral(n) {
    (sqrt(3) * sqrt(243*n**2 - 1) + 27*n)**(1/3) / 3**(2/3) + 1/(3**(1/3) * (sqrt(3) * sqrt(243*n**2 - 1) + 27*n)**(1/3)) - 1
}

#func isok(k, n) {
#    assert(binomial(k+2, 3) >= n!)
#    assert(!(binomial(k+1, 3) >= n!))
#    return true
#}

func find(k, n) {
     #a(n) = while (k*(k+1)*(k+2)/6 < n!, k++); k;

     while (binomial(k+2, 3) < n!) {
         ++k
     }

     return k
}

for k in (1..50) {

    var t = find(int(inverse_tetrahedral(k!)), k)

    #~ if (binomial(t+2, 3) == k!) {
        #~ say "Special: #{k}"
    #~ }

    print(t, ", ")

    #print(ceil(inverse_tetrahedral(k!)), ", ")
    #isok(t, k)
    #print(t, ", ")
}




# (sqrt(3) sqrt(243 n^2 - 1) + 27 n)^(1/3)/3^(2/3) + 1/(3^(1/3) (sqrt(3) sqrt(243 n^2 - 1) + 27 n)^(1/3)) - 1

#  (sqrt(3) * sqrt(243*(n!)^2 - 1) + 27*n!)^(1/3) / 3^(2/3) + 1/(3^(1/3) * (sqrt(3) * sqrt(243 * (n!)^2 - 1) + 27 * n!)^(1/3)) - 1

# a(n) = ceiling((sqrt(3) * sqrt(243*(n!)^2 - 1) + 27*n!)^(1/3) / 3^(2/3) + 1/(3^(1/3) * (sqrt(3) * sqrt(243 * (n!)^2 - 1) + 27 * n!)^(1/3)) - 1). - ~~~~