A074347 Smallest number requiring n steps to reach 0 when iterating the function: f(n)=abs(lpd(n)-Lpf(n)), where lpd(n) is the largest proper divisor of n and Lpf(n) is the largest prime factor of n.

1, 2, 3, 12, 13, 52, 53, 131, 271, 811, 1601, 2711, 8111, 13997, 34589, 74551, 147773, 310567, 621227, 1230343, 2627759, 4921373, 10741931, 24965191, 45887291, 111477631, 183638843, 394195667, 788380493, 1576798931

Offset

1,2

Comments

2*10^9 < a(31) <= 2938669883. a(32) <= 7511549827. a(33) <= 11754740251. a(34) <= 30050593523. - Donovan Johnson, Dec 22 2010

Links

Table of n, a(n) for n=1..30.

Jason Earls, Smarandache iterations of the first kind on functions involving divisors and prime factors, in Smarandache Notions Journal (2004), Vol. 14.1, page 259.

Prog

(PARI) {m=25; z=11000000; v=listcreate(m); for(i=1, m, listinsert(v, -1, i)); for(n=1, z, c=1; b=1; k=n; while(b&&c<=m, d=divisors(k); i=matsize(d)[2]-1; p=if(i>0, d[i], 1); q=if(k==1, 1, vecmax(component(factor(k), 1))); a=abs(p-q); if(a==0, b=0, k=a; c++)); if(a==0, if(v[c]<0, v[c]=n; print1([c, n])))); print(); for(i=1, m, print1(v[i], ", "))}

Crossrefs

Cf. A075660.

Sequence in context: A102660 A081347 A309176 * A102034 A102150 A039588

Adjacent sequences: A074344 A074345 A074346 * A074348 A074349 A074350

Keyword

more,nonn

Author

Jason Earls, Sep 23 2002

Extensions

Four more terms from Klaus Brockhaus, Oct 01 2002

a(24)-a(30) from Donovan Johnson, Dec 22 2010

Status

approved