A076423 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

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.

PROG

(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), ", "))}

CROSSREFS

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

Sequence in context: A322423 A325494 A295561 * A075660 A270788 A190496

Adjacent sequences: A076420 A076421 A076422 * A076424 A076425 A076426

KEYWORD

base,nonn

AUTHOR

Klaus Brockhaus, Oct 11 2002

STATUS

approved