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

[Don Reble]

> a(n) = 1,2,5,16,68,404,3587,51747,1343181,70863530...
>
> ... a(n) is the slowest growing integer sequence beginning with 1
> whose sequences of mth-order quotients are all strictly increasing,
> for all values of m.
>
> jon wild

    Perhaps Jon means _all_ values of m, including 0.
    (So that it can't begin 1,1.)  Or perhaps not,
        1 1 2  9 103 3405 371146 153037899 275315985020 2505668630734788
        1 2 5 16  68  404   3587     51747      1343181         70863530
    because the 1,1 sequence grows faster anyway. Jon?

    BTW, corresponding difference sequences are A000079 and A000225.

> ...take the product of the previous element a(n) and all of the most
> recently calculated mth ratios, add 1, and take the floor.
>
> --Graeme McRae

    Yes. The growth rate is hyperexponential, so my computer runs out of
    memory pretty quickly. (Those quotients are killers, not the sequence
    itself.) Have s'more terms.

1
2
5
16
68
404
3587
51747
1343181
70863530
8771738549
3010577465956
3472890614331263
16778636239137208665
435866021017987040200927
80724349462285706161330870948
146347653618405076026597153184017178
3702810253732678057039024884190121454618096
1941463904207501160190459589240443604643356373706327
32726487266841638505997450218899439615449730786589995293051657
28844658111712900956535374708852158563289732557889070099339337027912646286
2274694567010279910106522974702110180562161193985776880899521251905648932937035326556839
29007554702248633381369353553123095098328911275875177168688039684451424326676560888524834478778858475108
114654236288391623803120048812338378923201909025140523249822058948949003096097601289509973594977341379753585511691703312066
286771527322364315637265554893187362324790934083293394580448968848634100735335827561955127136999494818157671130578737141568527819282103471406137
991640462838273375627738696091672948855453024266252499046892313948814248377868053876458901350496387620054463160116560544010813779680789761429009802800978591899964162597

-- 
Don Reble  djr at nk.ca