cp's OEIS Frontend

A084144 First digit occurring consecutively exactly n times in Pi's decimal expansion.

%I A084144 #32 Feb 16 2025 08:32:49
%S A084144 3,3,1,7,0,9,3,4,7,6,1,7,8,9,6
%N A084144 First digit occurring consecutively exactly n times in Pi's decimal expansion.
%C A084144 A simple variation on this sequence could ignore the 3 before the decimal point, making a(1)=1 instead.
%C A084144 a(17) = 6. - _Dmitry Petukhov_, Oct 30 2021
%H A084144 Dave Andersen, <a href="http://www.angio.net/pi/piquery">Pi-Search Page</a>
%H A084144 Timothy Mullican, <a href="https://storage.googleapis.com/pi50t/index.html">50 trillion digits of pi</a>
%H A084144 Peter Trüb, <a href="https://pi2e.ch/blog/2017/03/10/pi-digits-download/">22.4 trillion digits of pi</a>
%H A084144 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PiDigits.html">Pi Digits.</a>
%e A084144 a(3) = 1 because the digit string <8>111<7>, where n=3, d=1, d1=8<>1 and d2=7<>1 in the following general form, occurs in the decimal expansion of Pi with a smaller starting index than all occurrences for n=3 of the string <d1>dd...d (n d's)<d2> for d=0, 2, 3, ..., or 9, where all of these n-digit strings are immediately preceded by some d1<>d and followed by some d2<>d. A049523(3) = 154 gives the starting index of this first occurrence of exactly three consecutive equal digits; i.e. the first 1 in this 111 is the 154th digit of Pi counting the 3 before the decimal point - add 1 to Pi-Search page result - but ignoring the decimal point itself. (<d1> is of course not completely applicable for the case n=1 in determining a(1).)
%Y A084144 Cf. A049523 (starting index), A084145 (consecutively at least n times).
%K A084144 nonn,base,more,hard
%O A084144 1,1
%A A084144 _Rick L. Shepherd_, May 15 2003
%E A084144 a(10)-a(11) from _Giovanni Resta_, Oct 02 2019
%E A084144 a(12)-a(14) added by _Dmitry Petukhov_, Jan 13 2020
%E A084144 a(15) from _Dmitry Petukhov_, Oct 30 2021