

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



