A194351 Starting position of the first occurrence of a string of 2^n in the decimal expansion of Pi.

1, 6, 2, 11, 40, 15, 22, 148, 1750, 1842, 12735, 26862, 27372, 2943, 37619, 39587, 106920, 820238, 76875, 47887, 6150809, 3660438, 17376657, 15416321, 162454456, 132295965, 265234498, 33844308, 4847933000, 671531549, 1122335995, 2894348872, 763748417

Offset

0,2

Comments

a(46) > 50*10^12. - _Dmitry Petukhov, Oct 27 2021

Links

Dmitry Petukhov, Table of n, a(n) for n = 0..45

Timothy Mullican, 50 trillion digits of pi

Peter Trüb, 22.4 trillion digits of pi

Formula

a(n) = A032445(2^n)-1. - R. J. Mathar, Sep 02 2011

Example

Pi = 3.141592653589793238462643383279502884197169399375105.. The '1' (2^0) after the decimal point is at position 1. The '1' of the first occurrence of '16' (2^4) is at position 40.

Mathematica

d = ToString[N[Pi-3, 1000000]]; Table[pos = StringPosition[d, ToString[2^n], 1]; If[pos == {}, Print["not enough digits for ", 2^n]; pos = 0, pos = pos[[1, 1]] - 2], {n, 0, 19}] (* T. D. Noe, Sep 02 2011 *)

Crossrefs

Cf. A000796, A176341, A193940.

Sequence in context: A357396 A100616 A097474 * A040035 A065272 A070394

Adjacent sequences: A194348 A194349 A194350 * A194352 A194353 A194354

Keyword

nonn,base

Author

Kausthub Gudipati, Aug 22 2011

Extensions

Terms corrected by D. S. McNeil, Sep 02 2011

a(29), a(32) from D. S. McNeil, Sep 03 2011

Edited by Hans Havermann, Jul 22 2014

a(28), a(30)-a(31) from Hans Havermann, Jul 22 2014

a(33)-a(43), a(45) from Dmitry Petukhov, Jan 27 2020

a(44) from Dmitry Petukhov, Oct 27 2021

Status

approved