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// https://oeis.org/A054554 | |
// https://www.youtube.com/watch?v=iFuR97YcSLM | |
for(int x = 2; x < 10; x++) { | |
//4n^2-2n+1 | |
def N = 4 * Math.pow(x, 2) - 2 * x + 1 | |
//ᒪ√((n+√(n-4)) / 4)ᒧ | |
def U = Math.floor(Math.sqrt((N + Math.sqrt(N - 4)) / 4)); | |
assert x == U | |
def u = U+1 // +1 para que se vea igual a https://oeis.org/A054554/b054554.txt | |
println String.format("%.0f -> %.0f", u, N) | |
} | |
//Comprobación | |
for(int x = 2; x < 9999; x++) { | |
def N = 4 * Math.pow(x, 2) - 2 * x + 1 | |
assert N == 4 * Math.pow(x, 2) - 2 * x + 1 | |
assert N - 1 == 4 * Math.pow(x, 2) - 2 * x | |
assert N - 1 == 2 * (2 * Math.pow(x, 2) - x) | |
assert (N - 1) / 2 == 2 * Math.pow(x, 2) - x | |
assert (N - 1) / 2 == x * (2 * x - 1) | |
//No se una mejor forma de despejar (-1), así que se busca su equivaliente en función de N; x=f(N) | |
assert (N - 1) / 2 != x * (2 * x) | |
assert ((N - 1) / 2) + (Math.sqrt(N)) != x * (2 * x) | |
assert ((N - 1) / 2) + (N + Math.sqrt(N)) != x * (2 * x) | |
assert ((N - 1) / 2) + ((N + Math.sqrt(N)) / 4) != x * (2 * x) | |
assert ((N - 1) / 2) + Math.sqrt((N + Math.sqrt(N)) / 4) != x * (2 * x) | |
assert ((N - 1) / 2) + Math.floor(Math.sqrt((N + Math.sqrt(N)) / 4)) == x * (2 * x) | |
assert ((N - 1) / 2) + Math.floor(Math.sqrt((N + Math.sqrt(N)) / 4)) == x * 2 * x | |
assert ((N - 1) / 2) + Math.floor(Math.sqrt((N + Math.sqrt(N)) / 4)) == Math.pow(x, 2) * 2 | |
assert (((N - 1) / 2) + Math.floor(Math.sqrt((N + Math.sqrt(N)) / 4))) / 2 == Math.pow(x, 2) | |
assert Math.sqrt((((N - 1) / 2) + Math.floor(Math.sqrt((N + Math.sqrt(N)) / 4))) / 2) == x | |
//La versión más corta que tengo | |
assert Math.floor(Math.sqrt((N + Math.sqrt(N - 4)) / 4)) == x | |
} |
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