A076426 Fixed points of the mapping k -> abs(reverse(lpd(k))-reverse(Lpf(k))). lpd(k) is the largest proper divisor and Lpf(k) is the largest prime factor of k.

5750, 33866, 74841, 517250, 577750, 5538710, 51414250, 51454250, 51687250, 51727250, 51748250, 51858250, 52525250, 57515750, 57535750, 57575750, 57757750, 67597352, 841794296, 5120202250, 5120802250, 5121612250

Offset: 1

Author

Klaus Brockhaus, Oct 11 2002

Keywords

• base
• nonn

Comments

Besides these fixed points (cycles of length 1) there are five cycles of length 2 ([9378, 9739], [518775, 522075], [5170250, 5197250], [5219475, 5249775], [5255750, 5755250]) and one cycle of length 3 ([7285, 7467, 9711]) below 8000000.

Examples

			lpd(5750) = 2875; Lpf(5750) = 23; 5782 - 32 = 5750.
		

Crossrefs

Cf. A076423, A076425.

Programs

PARI

{for(n=1,34000,v=divisors(n); a=matsize(v)[2]; z=if(a>1,v[a-1],1); p=0; while(z>0,d=divrem(z,10); z=d[1]; p=10*p+d[2]); z=if(n==1,1,vecmax(component(factor(n),1))); q=0; while(z>0,d=divrem(z,10); z=d[1]; q=10*q+d[2]); if(abs(p-q)==n,print1(n,",")))}

Formula

abs(reverse(lpd(n))-reverse(Lpf(n))) = n.

Extensions

Offset corrected and a(7)-a(22) from Donovan Johnson, Aug 09 2010