login
Exponent of least power of 2 having exactly n consecutive 7's in its decimal representation.
1

%I #18 Jul 20 2024 22:19:28

%S 0,15,27,24,181,317,2309,972,25264,131979,279275,279269,1727605,

%T 6030752,8760853,77235364

%N Exponent of least power of 2 having exactly n consecutive 7's in its decimal representation.

%H Popular Computing (Calabasas, CA), <a href="/A094776/a094776.jpg">Two Tables</a>, Vol. 1, (No. 9, Dec 1973), page PC9-16.

%e a(3)=24 because 2^24(i.e. 16777216) is the smallest power of 2 to contain a run of 3 consecutive sevens in its decimal form.

%t a = ""; Do[ a = StringJoin[a, "7"]; b = StringJoin[a, "7"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

%Y Cf. A006889, A131535, A131536, A131537, A131538, A131539, A131540, A131542, A131543.

%K more,nonn,base

%O 0,2

%A _Shyam Sunder Gupta_, Aug 26 2007

%E a(11)-a(12) from _Sean A. Irvine_, May 31 2010

%E a(13)-a(14) from _Lars Blomberg_, Jan 24 2013

%E a(15) from _Bert Dobbelaere_, Mar 02 2019

%E a(0)=0 prepended by _Paul Geneau de Lamarlière_, Jul 20 2024