A048940 Starting position of the first occurrence of a string of at least n '9's in the decimal expansion of Pi.

5, 44, 762, 762, 762, 762, 1722776, 36356642, 564665206, 20148132310, 27014073304, 897831316556, 5758910552709, 5758910552709

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base
• more

Comments

a(10) > 11*10^9 - 1. - Eric W. Weisstein, Jul 20 2013

a(15) > 22*10^12. - Dmitry Petukhov, Jan 29 2020

Pi digits 3,1,4,... are indexed 0,1,2,... Note that this is different from other sequences such as A049522, A084073 which use indices 1,2,3,... For example, the position of the curious accumulation of six 9s is called 762 here; the same position is called 763 in A049522, A084073. - Jeppe Stig Nielsen, Aug 21 2017

Links

• David G. Andersen, The Pi-Search Page. (Yields, as of today, an incorrect result of 66780105 for the first occurrence of eight "9"s. - _M. F. Hasler_, Mar 19 2017)
• Yasumasa Kanada Laboratory Home Page, Computer Centre, The University of Tokyo, Statistical Distribution Information
• PI-world Site, The digits and Statistics for 12 trillion digits of PI [archived page]
• Eric Weisstein's World of Mathematics, Feynman Point
• Eric Weisstein's World of Mathematics, Pi Digits

Crossrefs

Cf. A000796: Decimal expansion (or digits) of Pi.

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 exactly n times the same digit: A096755 (exactly n '1's), A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763 (exactly n '9's), A050279 (exactly n '0's).

First occurrence of n: A176341; of concatenate(1,...,n): A121280 = A068987 - 1.

Cf. A049522, A084073.

Programs

Mathematica

Module[{m, nn = 7}, m = First@ RealDigits@ N[Pi, 10^nn]; Array[ SequencePosition[m, ConstantArray[9, #]][[1, 1]] - 1 &, nn]] (* Michael De Vlieger, Mar 20 2017 *)

Extensions

More terms from Colin Martin (cbmartin(AT)tpg.com.au), Mar 03 2002

Edited by M. F. Hasler, Mar 19 2017

a(10)-a(11) from Giovanni Resta, Sep 30 2019

a(12) from Yasumasa Kanada Laboratory, 2002 and a(13)-a(14) from Shigeru Kondo, 2011 added by Dmitry Petukhov, Dec 23 2019