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A288966 a(n) = the number of iterations the "HyperbolaTiles" algorithm takes to factorize n. 2
1, 2, 4, 3, 8, 4, 12, 5, 8, 6, 20, 7, 24, 8, 12, 9, 32, 10, 36, 11, 16, 12, 44, 13, 24, 14, 20, 15, 56, 16, 60, 17, 24, 18, 32, 19, 72, 20, 28, 21, 80, 22, 84, 23, 32, 24, 92, 25, 48, 26, 36, 27, 104, 28, 48, 29, 40, 30, 116, 31, 120, 32, 44, 33, 56, 34, 132 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The provided "HyperbolaTiles" algorithm computes a factorization of n and computes a(n), the number of required iterations to reach this factorization.

If n = 1, the factorization is considered reached with (n=1*1).

If n is prime, the factorization is considered reached with (n=n*1).

If n is compound, the exhibited factorization is (n=p*q) with p least prime divisor of n.

LINKS

Table of n, a(n) for n=1..67.

Luc Rousseau, Proof that the algorithm performs integer factorisation

PROG

(Java)

package oeis;

public class A {

public static void main(String[] args) {

for (int n = 1; n <= 67; n ++) { hyberbolaTiles(n); }

}

private static void hyberbolaTiles(int n) {

int i = 0, x = 0, y = 0, p = 0, q = n;

do {

i ++;

if (y < 0) { x = y + q; q --; }

if (y > 0) { p ++; x = y - p; }

if (y == 0) {

p ++;

x = 0;

if ((p != 1) || (q == 1)) {

System.out.print("" + i + " // " + n + " = " + p + " * " + q);

break;

}

q --;

}

y = x + p - q;

} while (q > 0);

}

}

CROSSREFS

Sequence in context: A324213 A052131 A051145 * A057495 A321366 A180246

Adjacent sequences:  A288963 A288964 A288965 * A288967 A288968 A288969

KEYWORD

nonn

AUTHOR

Luc Rousseau, Jun 20 2017

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)