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First digit occurring consecutively at least n times in Pi's decimal expansion.
2

%I #23 Oct 30 2021 13:12:32

%S 3,3,1,9,9,9,3,4,7,6,1,7,8,9,6,6,6

%N First digit occurring consecutively at least n times in Pi's decimal expansion.

%C A simple variation on this sequence could ignore the 3 before the decimal point, making a(1)=1 instead.

%H Dave Andersen, <a href="http://www.angio.net/pi/piquery">Pi-Search Page</a>

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

%H Peter TrĂ¼b, <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>

%e a(4)=a(5)=a(6) = 9 because there are (exactly) six consecutive 9's occurring with starting index A049522(4)=A049522(5)=A049522(6) = 763 and there are no runs of 4, 5, 6, or more consecutive equal digits having a smaller starting index.

%e The first occurrence of a run of at least seven consecutive equal digits occurs at starting index A049522(7) = 710101. The run consists of exactly seven 3's so a(7) = 3 [=A084144(7)] and also A049523(7) = 710101.

%Y Cf. A049522 (starting index), A084144 (consecutively exactly n times), A049523 (starting index for A084144 runs).

%K base,nonn,more

%O 1,1

%A _Rick L. Shepherd_, May 23 2003

%E a(10)-a(14) added by _Dmitry Petukhov_, Jan 13 2020

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