"More"-Cam [A034995]

[Hans Havermann]

on 6/15/01 12:23 PM, Richard Guy wrote:

> Is the next member of A034995
> 999999999956753113201 (= 31622776601^2 ) ??

I think so...

Smallest squares starting with a string of n 9's:

9, 99225, 9991921, 999950884, 99999515529, 9999995824729, 999999961946176,
99999999356895225, 99999999989350756, 999999999956753113201,
99999999999470044512256, 9999999999991276338467889,
999999999999949826038432489, 99999999999999409792567484569,
9999999999999991575699311150884, 999999999999999916516569555499264,
99999999999999999241123339954036624, 9999999999999999993682442519108007561,
999999999999999999937454230741109035761,
99999999999999999999437522862413986373601,
9999999999999999999994348728804092706672004,
999999999999999999999940837306036211360320144,
99999999999999999999999143374859890542963212544,
9999999999999999999999990232149833095400289227664,
999999999999999999999999908652728156686241882456356,
99999999999999999999999999087194732106410451442758609,
9999999999999999999999999990938692375018907776247092849,
999999999999999999999999999916061429145669403944421606249,
99999999999999999999999999999195609298971050791239505131364,
9999999999999999999999999999995455593741146183091923958202624,
999999999999999999999999999999925032693334823829032263045594276,
99999999999999999999999999999999460280185852817433623870357179441,
9999999999999999999999999999999990299905827639054010371545340002089,
999999999999999999999999999999999915428327611051613996844726441369856,
99999999999999999999999999999999999132299145509271796481817150775509904,
9999999999999999999999999999999999995449133715305042280152947232801672089,
999999999999999999999999999999999999924386690750709747855161948612093432896,
...

and A034994, their square roots:

3, 315, 3161, 31622, 316227, 3162277, 31622776, 316227765, 316227766,
31622776601, 316227766016, 3162277660167, 31622776601683, 316227766016837,
3162277660168378, 31622776601683792, 316227766016837932,
3162277660168379331, 31622776601683793319, 316227766016837933199,
3162277660168379331998, 31622776601683793319988, 316227766016837933199888,
3162277660168379331998892, 31622776601683793319988934,
316227766016837933199889353, 3162277660168379331998893543,
31622776601683793319988935443, 316227766016837933199889354442,
3162277660168379331998893544432, 31622776601683793319988935444326,
316227766016837933199889354443271, 3162277660168379331998893544432717,
31622776601683793319988935444327184, 316227766016837933199889354443271852,
3162277660168379331998893544432718533,
31622776601683793319988935444327185336,
...