login
Smallest starting index for a run of at least n consecutive equal digits in decimal expansion of Pi.
13

%I #39 Oct 30 2021 07:12:20

%S 1,25,154,763,763,763,710101,22931746,24658602,386980413,15647738229,

%T 368299898267,2164164669333,5758910552710,28642224609576,

%U 28642224609576,28642224609576

%N Smallest starting index for a run of at least n consecutive equal digits in decimal expansion of Pi.

%C Digits 3,1,4,1,5,... are indexed 1,2,3,4,5,...

%C a(11) > 2*10^9. - _M. F. Hasler_, Mar 21 2017

%C a(12) > 99*10^9. - _Giovanni Resta_, Oct 02 2019

%C a(15) > 12*10^12. - _Dmitry Petukhov_, Dec 30 2019

%C a(18) > 50*10^12. - _Dmitry Petukhov_, Oct 30 2021

%H <a href="http://www.subidiom.com/pi/">Pi search engine</a> (searches initial 2 x 10^9 digits of Pi)

%H Dave Andersen, <a href="http://www.angio.net/pi/piquery">Pi-Search Page</a> (searches initial 2 x 10^8 digits of Pi)

%H Yasumasa Kanada, <a href="http://www.super-computing.org/pi-decimal_current.html">Statistical Distribution Information</a>, Home page, Computer Centre, The University of Tokyo.

%H Timothy Mullican, <a href="https://storage.googleapis.com/pi50t/index.html">50 trillion digits of pi</a>

%H PI-world Site, <a href="https://web.archive.org/web/20140130074648/http://piworld.calico.jp/epidigits.html">The digits and Statistics for 12 trillion digits of PI</a> [archived page]

%H Peter Trüb, <a href="https://pi2e.ch/blog/2017/03/10/pi-digits-download/">22.4 trillion digits of pi</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiDigits.html">Pi Digits.</a>

%Y Cf. A049514-A049523.

%Y Compare A049523: the first run of six 9's occurs (with starting index 763) before any runs of exactly four or exactly five equal digits.

%Y Cf. A084145 (digit with this starting index).

%K nonn,base,more

%O 1,2

%A _Harvey P. Dale_

%E More terms from _Rick L. Shepherd_, May 22 2003

%E a(10) from _Felix Fröhlich_, Oct 06 2016

%E a(11) from _Giovanni Resta_, Oct 02 2019

%E a(12)-a(14) added by _Dmitry Petukhov_, Dec 30 2019

%E a(15)-a(17) from _Dmitry Petukhov_, Oct 30 2021