A346593 Numbers k such that A006577(k^3) sets a new record.

2, 3, 6, 7, 14, 15, 25, 41, 45, 71, 79, 153, 233, 235, 470, 503, 707, 741, 1482, 2964, 3039, 3581, 7162, 14324, 27337, 54674, 61683, 123366, 168159, 254251, 302839, 605678, 622699, 947173, 1618687, 3237374, 6474748, 10995401, 13042083, 21767875, 43535750, 48584565

Offset: 1

Author

Hugo Pfoertner, Jul 28 2021

Keywords

• nonn

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006577, A006877, A244638, A346591, A346592.

Programs

Mathematica

s[n_]:=s[n]=(i=0;r=n;While[r!=1,i++;If[EvenQ@r,r=r/2,r=r*3+1]];i);
lst={};max=1;Do[t=s[k^3];If[t>max,AppendTo[lst,k];max=t],{k,10^4}];lst (* Giorgos Kalogeropoulos, Jul 28 2021 *)

PARI

a6577(n0)={my(n=n0,k=0);while(n>1,k++;n=if(n%2,3*n+1,n/2));k};
a346593(limit)={msteps=0;for(k=1,limit,my(m=a6577(k^3));if(m>msteps,print1(k,", ");msteps=m))};
a346593(1000000)