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

3, 3, 1, 7, 0, 9, 3, 4, 7, 6, 1, 7, 8, 9, 6

Offset

1,1

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

Links

Table of n, a(n) for n=1..15.

Dave Andersen, Pi-Search Page

Timothy Mullican, 50 trillion digits of pi

Peter Trüb, 22.4 trillion digits of pi

Eric Weisstein's World of Mathematics, Pi Digits.

Example

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).

Sequence in context: A234251 A049323 A322148 * A306759 A214362 A180735

Adjacent sequences: A084141 A084142 A084143 * A084145 A084146 A084147

Keyword

nonn,base,more

Author

Rick L. Shepherd, May 15 2003

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

Status

approved