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%I #20 May 27 2021 01:55:35
%S 5,25,83,219,221,2270,11020,18843,192915,271978,743748,1039315,
%T 13873203,14060685
%N Least exponent k such that 2^k has exactly n consecutive 3's in its decimal representation.
%C No more terms < 28*10^6.
%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) = 83 because 2^83 (= 9671406556917033397649408) is the smallest power of 2 to contain a run of exactly 3 consecutive threes in its decimal form.
%t a = ""; Do[ a = StringJoin[a, "3"]; b = StringJoin[a, "3"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 9} ]
%o (Python)
%o def a(n):
%o k, n2, np2 = 1, '3'*n, '3'*(n+1)
%o while True:
%o while not n2 in str(2**k): k += 1
%o if np2 not in str(2**k): return k
%o k += 1
%o print([a(n) for n in range(1, 9)]) # _Michael S. Branicky_, May 25 2021
%Y Cf. A000079.
%K nonn,base,more
%O 1,1
%A _Shyam Sunder Gupta_, Aug 26 2007
%E a(10)-a(12) from _Sean A. Irvine_, Jul 19 2010
%E a(13)-a(14) from _Lars Blomberg_, Jan 24 2013
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