A096764 -id:A096764 - cp's OEIS frontend

A050279 a(n) is the starting position of the first occurrence of a string of at least n '0's in the decimal expansion of Pi.

32, 307, 601, 13390, 17534, 1699927, 3794572, 172330850, 2542542102, 8324296435, 371247087572, 1755524129973, 3186699229890, 6381820482331

Offset: 1

Eric W. Weisstein

At least up to a(10), also the starting position of the first occurrence of a string of exactly n '0's in the decimal expansion of Pi, cf. A096764. - M. F. Hasler, Mar 19 2017, edited Sep 03 2017

a(15) > 22*10^12. - Dmitry Petukhov, Jan 28 2020

Shigeru Kondo, calculation of Pi to 12.8 * 10^9 digits, using the program PiFast of Xavier Gourdon

David G. Andersen, The Pi-Search Page.
Peter Trüb, 22.4 trillion digits of pi
Eric Weisstein's World of Mathematics, Pi Digits

See A096764 for another version.
Cf. A000796: Decimal expansion (or digits) of Pi.
First occurrence of exactly n times the same digit: A096755 (exactly n '1's), A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763 (exactly n '9's), A096764 (exactly n '0's).
First occurrence of n times the same digit: A035117 (n '1's), A050281 (n '2's), A050282, A050283, A050284, A050286, A050287, A048940 (n '9's).
First occurrence of concatenate(1,...,n): A121280 = A068987 - 1.

More terms from Colin B. Martin (martinc(AT)ram.net.au), Nov 25 2001
Edited by N. J. A. Sloane at the suggestion of M. F. Hasler, Aug 24 2007
Edited by M. F. Hasler, Mar 19 2017
Definition modified by N. J. A. Sloane, Sep 03 2017
a(11)-a(14) added by Dmitry Petukhov, Jan 12 2020

A096755 Index of first occurrence of exactly n consecutive '1's in a row in the decimal expansion of Pi.

Original entry on oeis.org

1, 94, 153, 12700, 32788, 255945, 4657555, 159090113, 812432526, 3961184001, 15647738228, 1041032609981, 3907688331257, 68635742334547

Offset: 1

Robert G. Wilson v, Jul 07 2004

Presently identical to A035117.

It would be interesting to know the source for a(10) ~ 4*10^9, since the angio.net web site only searches up to 200M digits of Pi and even on subidiom.com only 2e9 digits of Pi are available. - M. F. Hasler, Apr 13 2019

David G. Andersen, The Pi-Search Page.
Yasumasa Kanada, Statistical Distribution Information, Home page, Computer Centre, The University of Tokyo.
PI-world Site, The digits and Statistics for 12 trillion digits of PI [archived page]
Peter Trüb, 22.4 trillion digits of pi

Cf. A035117, A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763, A096764.

a(11) from Giovanni Resta, Sep 30 2019
a(12) from Yasumasa Kanada, 2002 and a(13) from Shigeru Kondo, 2011, added by Dmitry Petukhov, Dec 27 2019
a(14) from Dmitry Petukhov, Sep 19 2022

A086639 Write decimal expansion of Pi in triangular form; sequence gives left edge.

Original entry on oeis.org

3, 1, 1, 2, 5, 3, 2, 2, 4, 9, 9, 7, 8, 3, 8, 7, 2, 1, 8, 9, 5, 3, 6, 6, 3, 5, 7, 6, 2, 2, 9, 9, 4, 0, 4, 2, 3, 0, 4, 1, 6, 7, 8, 9, 9, 1, 2, 3, 0, 1, 7, 2, 2, 4, 7, 8, 3, 1, 8, 3, 0, 2, 7, 9, 1, 6, 2, 2, 6, 7, 6, 8, 1, 5, 7, 3, 7, 7, 2, 4, 9, 3, 2, 1, 9, 8, 9, 1, 2, 7, 7, 9, 4, 0, 9, 2, 9, 8, 4, 9, 9, 2, 0, 7, 0

Offset: 1

Cino Hilliard, Jul 24 2003

In the second formula, "if" can most probably be strengthened to "if and only if": Indeed, a(n) = 0 can be equal to A000030(A090897(n)) only if A090897(n) = 0, i.e., there would be a string of n consecutive zeros in the decimals of Pi from position T(n-1)+1 to position T(n). The probability that this happens appears to be zero. (Notice how A096764(n), first occurrence of n consecutive zeros, grows incredibly much faster than T(n).) Maybe this could be proved considering, e.g., a continued fraction expansion of Pi whose coefficients follow some pattern of moderate growth (as e.g. in A046126), while a very long string of zeros in the decimal expansion would mean that it is exceptionally close to the rational number given by the truncation. - M. F. Hasler, Jan 06 2023

			Triangle is
  3
  14
  159
  2653
  58979
  323846
  2643383
  27950288
  419716939
  9375105820
a(34) = 0 because in the decimals of Pi there is a 0 at position 562, following the triangular number A000217(33) = 561, i.e., in the first column of the 34th row in the above triangle. - _Michel Marcus_ and _M. F. Hasler_, Jan 06 2023

Cf. A000796, A083437.

Cf. A000030, A090897.

pi = RealDigits[Pi, 10, 5461][[1]]; Table[ pi[[n(n + 1)/2 + 1]], {n, 0, 104}]
Module[{nn=110,pid},pid=RealDigits[Pi,10,(nn(nn+1))/2][[1]];TakeList[ pid,Range[ nn]]][[;;,1]] (* Harvey P. Dale, Mar 06 2023 *)

a(n) = A000796(1-n(n-1)/2). - M. F. Hasler, Oct 20 2011

a(n) = A000030(A090897(n)) if (and probably only if) a(n) is nonzero. - Michel Marcus and M. F. Hasler, Jan 06 2023

Edited by Robert G. Wilson v, Jul 26 2003

cp's OEIS Frontend

A050279 a(n) is the starting position of the first occurrence of a string of at least n '0's in the decimal expansion of Pi.

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A096755 Index of first occurrence of exactly n consecutive '1's in a row in the decimal expansion of Pi.

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Author

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Extensions

A086639 Write decimal expansion of Pi in triangular form; sequence gives left edge.

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