A131536 - OEIS

%I #24 Jul 20 2024 20:10:47

%S 0,1,51,43,692,314,2354,8555,13326,81784,279272,865356,1727608,

%T 1727602,23157022,63416790

%N Exponent of least power of 2 having exactly n consecutive 2'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)=43 because 2^43(i.e. 8796093022208) is the smallest power of 2 to contain a run of 3 consecutive twos in its decimal form.

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

%o (Python)

%o def A131536(n):

%o     s, t, m, k, u = '2'*n, '2'*(n+1), 0, 1, '1'

%o     while s not in u or t in u:

%o         m += 1

%o         k *= 2

%o         u = str(k)

%o     return m # _Chai Wah Wu_, Jan 28 2020

%Y Cf. A006889, A131535, A259089.

%K more,nonn,base

%O 0,3

%A _Shyam Sunder Gupta_, Aug 26 2007

%E 3 more terms from _Sean A. Irvine_, Jul 19 2010

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

%E a(15) from _Bert Dobbelaere_, Feb 25 2019

%E a(0) from _Chai Wah Wu_, Jan 28 2020