[seqfan] Re: slowest-growing "accelerating" sequence

[Hans Havermann]

Don Reble: "The growth rate is hyperexponential, so my computer runs out of memory pretty quickly."
"… (term #26) 991640462838273375627738696091672948855453024266252499046892313948814248377868053876458901350496387620054463160116560544010813779680789761429009802800978591899964162597"

Using exact integer arithmetic, I can get term #30 on my system, but just barely, and it took 23.5 hours for that final step. By relaxing our stance to arbitrary precision arithmetic, we can do much better. In Mathematica,

t=Table[{1,1},{100}]; Print[1]; Do[m=1;Do[m=m*t[[i,2]],{i,v}]; n=Floor[m+1]; Print[n]; 
 Do[t[[i,1]]=t[[i,2]],{i,v}]; t[[1,2]]=N[n,1000000]; Do[t[[i+1,2]]=t[[i,2]]/t[[i,1]],{i,v}], {v,99}]

generates 100 terms through approximation (that's the N[n,1000000] part), in about 7.5 minutes on my iMac. Term #129 appears to be the first one with more than a million digits; term #317, more than a billion; and term #704, more than a trillion.