A083630
Starting positions of strings of eight '6's in the decimal expansion of Pi.
Original entry on oeis.org
45681781, 45681782, 55616210, 129423072, 160301327, 320800854, 354039866, 386980412, 386980413, 386980414, 424213905, 424213906, 661180039, 823960247, 864397328, 923385691, 1064174618, 1129615231, 1183548825, 1208233597, 1261092402, 1311369257
Offset: 1
More terms, via Taylor's search engine, from
M. F. Hasler, Mar 21 2017
A083636
Starting positions of strings of eight 7's in the decimal expansion of Pi.
Original entry on oeis.org
24658601, 24658602, 82144203, 287248607, 1096547723, 1136093224, 1136093225, 1199887625, 1253506894, 1284344221, 1284344222, 1343455078, 1347842020, 1387894932, 1387894933, 1439845247, 1577148578
Offset: 1
A084073
Starting index of a record-breaking string of consecutive equal digits in the decimal expansion of Pi.
Original entry on oeis.org
1, 25, 154, 763, 710101, 22931746, 24658602, 386980413
Offset: 1
The repeated digits are 3, 3, 1, 6, 3, 4, 7, ..., i.e., at position a(1) = 1, there is one '3', starting at position a(2) = 25, there are two '3's, from position a(3) = 154 on, there are three '1's, etc.
A084144
First digit occurring consecutively exactly n times in Pi's decimal expansion.
Original entry on oeis.org
3, 3, 1, 7, 0, 9, 3, 4, 7, 6, 1, 7, 8, 9, 6
Offset: 1
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).)
Cf.
A049523 (starting index),
A084145 (consecutively at least n times).
A084145
First digit occurring consecutively at least n times in Pi's decimal expansion.
Original entry on oeis.org
3, 3, 1, 9, 9, 9, 3, 4, 7, 6, 1, 7, 8, 9, 6, 6, 6
Offset: 1
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.
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.
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