A076423 Number of iterations of the mapping k -> abs(reverse(lpd(k))-reverse(gpf(k))) to reach zero, or -1 if zero is never reached. lpd(k) is the largest proper divisor and gpf(k) is the greatest prime factor of k.

1, 2, 3, 1, 2, 1, 2, 3, 1, 1, 2, 4, 3, 1, 1, 2, 3, 2, 3, 2, 1, 1, 6, 3, 1, 1, 2, 2, 2, 2, 5, 3, 1, 1, 1, 3, 5, 1, 1, 4, 4, 3, 2, 3, 2, 1, 5, 2, 1, 6, 1, 6, 2, 2, 1, 7, 1, 1, 2, 3, 2, 1, 3, 2, 1, 2, 7, 3, 1, 2, 3, 4, 4, 1, 6, 4, 1, 2, 4, 2, 2, 1, 6, 4, 1, 1, 1, 2, 4, 2, 1, 4, 1, 1, 1, 3, 3, 2, 2, 1, 2, 8, 3, 2, 2

Offset: 1

Author

Klaus Brockhaus, Oct 11 2002

Keywords

• base
• nonn

Comments

See A076425 for numbers such that zero is never reached, A076424 for the smallest number that needs n iterations to reach zero, A076426 for fixed points of the mapping.

Examples

			For n = 13: lpd(13) = 1, gpf(13)=13, abs(reverse(1)-reverse(13)) = 30; lpd(30) = 15, gpf(30) = 5, abs(reverse(15)-reverse(5)) = 46; lpd(46) = 23, gpf(46)=23, abs(reverse(23)-reverse(23)) = 0. Three iterations to reach zero, so a(13) = 3.
		

Crossrefs

Cf. A032742, A006530, A075660, A076424, A076425, A076426.

Programs

PARI

{stop=20; for(n=1,105,c=1; b=1; k=n; while(b&&c<=stop,w=divisors(k); s=matsize(w)[2]-1; z=if(s>0,w[s],1); p=0; while(z>0,d=divrem(z,10); z=d[1]; p=10*p+d[2]); z=if(k==1,1,vecmax(component(factor(k),1))); q=0; while(z>0,d=divrem(z,10); z=d[1]; q=10*q+d[2]); k=abs(p-q); if(k>0,c++,b=0)); print1(if(c>stop,-1,c),","))}