cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A049522 Smallest starting index for a run of at least n consecutive equal digits in decimal expansion of Pi.

Original entry on oeis.org

1, 25, 154, 763, 763, 763, 710101, 22931746, 24658602, 386980413, 15647738229, 368299898267, 2164164669333, 5758910552710, 28642224609577, 28642224609577, 28642224609577
Offset: 1

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Author

Keywords

Comments

Digits 3,1,4,1,5,... are indexed 1,2,3,4,5,...
a(11) > 2*10^9. - M. F. Hasler, Mar 21 2017
a(12) > 99*10^9. - Giovanni Resta, Oct 02 2019
a(15) > 12*10^12. - Dmitry Petukhov, Dec 30 2019
a(18) > 50*10^12. - Dmitry Petukhov, Oct 30 2021

Crossrefs

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

Extensions

More terms from Rick L. Shepherd, May 22 2003
a(10) from Felix Fröhlich, Oct 06 2016
a(11) from Giovanni Resta, Oct 02 2019
a(12)-a(14) added by Dmitry Petukhov, Dec 30 2019
a(15)-a(17) from Dmitry Petukhov, Oct 30 2021
a(15)-a(17) had off-by-1 error, corrected by Mike Keith, Feb 03 2025

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

Views

Author

Rick L. Shepherd, May 15 2003

Keywords

Comments

A simple variation on this sequence could ignore the 3 before the decimal point, making a(1)=1 instead.
a(17) = 6. - Dmitry Petukhov, Oct 30 2021

Examples

			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).)
		

Crossrefs

Cf. A049523 (starting index), A084145 (consecutively at least n times).

Extensions

a(10)-a(11) from Giovanni Resta, Oct 02 2019
a(12)-a(14) added by Dmitry Petukhov, Jan 13 2020
a(15) from Dmitry Petukhov, Oct 30 2021
Showing 1-2 of 2 results.