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

%I #47 Oct 28 2021 02:02:39

%S 1,6,2,11,40,15,22,148,1750,1842,12735,26862,27372,2943,37619,39587,

%T 106920,820238,76875,47887,6150809,3660438,17376657,15416321,

%U 162454456,132295965,265234498,33844308,4847933000,671531549,1122335995,2894348872,763748417

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

%C a(46) > 50*10^12. - __Dmitry Petukhov_, Oct 27 2021

%H Dmitry Petukhov, <a href="/A194351/b194351.txt">Table of n, a(n) for n = 0..45</a>

%H Timothy Mullican, <a href="https://storage.googleapis.com/pi50t/index.html">50 trillion digits of pi</a>

%H Peter TrĂ¼b, <a href="https://pi2e.ch/blog/2017/03/10/pi-digits-download/">22.4 trillion digits of pi</a>

%F a(n) = A032445(2^n)-1. - _R. J. Mathar_, Sep 02 2011

%e 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.

%t 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 *)

%Y Cf. A000796, A176341, A193940.

%K nonn,base

%O 0,2

%A _Kausthub Gudipati_, Aug 22 2011

%E Terms corrected by _D. S. McNeil_, Sep 02 2011

%E a(29), a(32) from _D. S. McNeil_, Sep 03 2011

%E Edited by _Hans Havermann_, Jul 22 2014

%E a(28), a(30)-a(31) from _Hans Havermann_, Jul 22 2014

%E a(33)-a(43), a(45) from _Dmitry Petukhov_, Jan 27 2020

%E a(44) from _Dmitry Petukhov_, Oct 27 2021