Re: series puzzle

From	richard@cogsci.ed.ac.uk (Richard Tobin)
Newsgroups	rec.puzzles
Subject	Re: series puzzle
Date	2026-08-30 12:06 +0000
Organization	HCRC, University of Edinburgh
Message-ID	<11716b8$79li$2@artemis.inf.ed.ac.uk> (permalink)
References	<8733vz45sz.fsf@asdf.ee> <116so5c$4t1g$1@artemis.inf.ed.ac.uk>

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In article <116so5c$4t1g$1@artemis.inf.ed.ac.uk>,
Richard Tobin <richard@cogsci.ed.ac.uk> wrote:
>In article <8733vz45sz.fsf@asdf.ee>, Phil Carmody  <pc+usenet@asdf.org> wrote:
>
>>Bonus points for the mathmos: give an expression for how quickly this
>>series grows: how many digits would you expect the 1000th, 10000th,
>>100000th, and 1000000th terms to have?

>    1000 167268718788585637957754176512
>   10000 115561287648644129422797664757359949255136
>  100000 1136141149823685669283941799894965343754256
> 1000000 1114828839832196352142477728158415189411298271623636456323512734248

Some more values:

10000000 11369436279154838514569735263935293883868829566247715738211151771131572
100000000 111892791617298738664974975189485467758117557576382896636315253382745554253755326351157248
1000000000 1116261265478134227397932673264932225965498386448886515479288939874744881126242351158526
10000000000 11115592733643186436631888321432897482694847579734846162383383488896288842919911525326836588516428648
100000000000 11116293777537955511862692148592837467885749363711973614574829888862236243951212275792322432572882368424424384

It's amazing what you can do with brute force these days.

In terms of number of digits:

10^3 30
10^4 42
10^5 43
10^6 67
10^7 71
10^8 90
10^9 88
10^10 101
10^11 110

Which is in accordance with my hand-waving estimate of the growth rate
and Sloane's "very crude calculation".

-- Richard

Thread

series puzzle Phil Carmody <pc+usenet@asdf.org> - 2026-08-28 00:22 +0300
  Re: series puzzle David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-08-28 08:56 +0000
  Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-08-28 17:54 +0000
  Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-08-28 19:39 +0000
    Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-08-28 19:49 +0000
      Re: series puzzle David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-08-30 08:49 +0000
        Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-08-30 11:51 +0000
    Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-08-30 12:06 +0000
      Re: series puzzle Phil Carmody <pc+usenet@asdf.org> - 2026-09-01 12:14 +0300
        Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-09-01 10:03 +0000
          Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-09-05 10:11 +0000
            Re: series puzzle richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-09-05 10:51 +0000
              Re: series puzzle David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-09-06 07:52 +0000
    Re: series puzzle Phil Carmody <pc+usenet@asdf.org> - 2026-08-31 22:22 +0300

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