%I #5 Aug 04 2021 07:44:16
%S 2,3,4,5,7,8,9,11,12,14,17,21,26,29,33,34,37,44,45,47,48,51,52,55,58,
%T 61,70,78,85,89,91,92,93,96,97,98,105,107,113,114,118,124,129,135,145,
%U 148,149,150,152,157,161,173,175,179,184,192,201,205,206,209,212,213
%N Numbers k such that A006577(k!) sets a new record.
%o (PARI) a6577(n0)={my(n=n0,k=0);while(n>1,k++;n=if(n%2,3*n+1,n/2));k};
%o a346782(limit)={my(msteps=0);for(k=0,limit,my(m=a6577(k!));if(m>msteps,print1(k,", ");msteps=m))};
%o a346782(215)
%Y The corresponding record numbers of steps are A346783.
%Y Cf. A006577, A070974, A346592, A346593.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Aug 04 2021