A076426 -id:A076426 - cp's OEIS frontend

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

Klaus Brockhaus, Oct 11 2002

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.

			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.

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

{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),","))}

A076425 Numbers n such that zero is never reached by iterating the mapping k -> abs(reverse(lpd(k))-reverse(gpf(k))). lpd(k) is the largest proper divisor and gpf(k) is the largest prime factor of k.

Original entry on oeis.org

2074, 2113, 2179, 2914, 3111, 4112, 4371, 4390, 4456, 4956, 4978, 5185, 5450, 5750, 6474, 6585, 6827, 7248, 7259, 7285, 7467, 8175, 8625, 8647, 9378, 9711, 9739, 10199, 10975, 11407, 11752, 12006, 12232, 12338, 12445, 12826, 13224, 13396

Offset: 1

Klaus Brockhaus, Oct 11 2002

n such that A076423(n) = -1.

			For 4112 the mapping leads to a fixed point (cf. A076426): 4112 -> 5750 -> 5750 -> ...; for 2074 the mapping leads to a cycle: 2074 -> 7285 -> 7467 -> 9711 -> 7285 -> ...

Cf. A076423, A076426.

{stop=20; for(n=1,13600,c=1; b=1; k=n; while(b&&c1,v[a-1],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]); a=abs(p-q); if(a==0,b=0,k=a; c++)); if(a>0,print1(n,",")))}

cp's OEIS Frontend

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.

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