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A259092 Smallest k such that 2^k contains three adjacent copies of n in its decimal expansion.

%I A259092 #25 Sep 30 2024 15:48:16
%S A259092 242,42,43,83,44,41,157,24,39,50,949,1841,3661,1798,1701,1161,1806,
%T A259092 391,1890,2053,950,1164,2354,1807,3816,1800,1799,818,1702,2115,904,
%U A259092 1798,1807,2270,392,1699,3022,394,2054,1758,1804,2300,2720,2403,3396,1133,1808,3820
%N A259092 Smallest k such that 2^k contains three adjacent copies of n in its decimal expansion.
%C A259092 The multi-digit generalization of A171242. - _R. J. Mathar_, Jul 06 2015
%H A259092 Chai Wah Wu, <a href="/A259092/b259092.txt">Table of n, a(n) for n = 0..1000</a>
%H A259092 Popular Computing (Calabasas, CA), <a href="/A094776/a094776.jpg">Two Tables</a>, Vol. 1, (No. 9, Dec 1973), page PC9-16.
%e A259092 2^242 = 7067388259113537318333190002971674063309935587502475832486424805170479104 contains three adjacent 0's.
%t A259092 Table[k = 0; While[! SequenceCount[IntegerDigits[2^k], Flatten[ConstantArray[IntegerDigits[n], 3]]] > 0, k++]; k, {n, 0, 50}] (* _Robert Price_, May 17 2019 *)
%o A259092 (Python)
%o A259092 def A259092(n):
%o A259092     s, k, k2 = str(n)*3, 0, 1
%o A259092     while True:
%o A259092         if s in str(k2):
%o A259092             return k
%o A259092         k += 1
%o A259092         k2 *= 2 # _Chai Wah Wu_, Jun 18 2015
%Y A259092 Cf. A006889, A131535, A131536, A259089, A063565, A259091.
%K A259092 nonn,base
%O A259092 0,1
%A A259092 _N. J. A. Sloane_, Jun 18 2015
%E A259092 More terms from _Chai Wah Wu_, Jun 18 2015