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A259091 Smallest k such that 2^k contains two adjacent copies of n in its decimal expansion.

%I A259091 #22 Sep 30 2024 15:25:31
%S A259091 53,40,43,25,18,16,46,24,19,33,378,313,170,374,361,359,64,34,507,151,
%T A259091 348,246,314,284,349,314,261,151,385,166,156,364,65,219,371,359,503,
%U A259091 148,155,352,349,308,247,255,192,387,165,149,171,150,210,155,209,101,505
%N A259091 Smallest k such that 2^k contains two adjacent copies of n in its decimal expansion.
%C A259091 The multi-digit generalization of A171132. - _R. J. Mathar_, Jul 06 2015
%H A259091 Chai Wah Wu, <a href="/A259091/b259091.txt">Table of n, a(n) for n = 0..1000</a>
%H A259091 Popular Computing (Calabasas, CA), <a href="/A094776/a094776.jpg">Two Tables</a>, Vol. 1, (No. 9, Dec 1973), page PC9-16.
%e A259091 2^53 = 9007199254740992 contains two adjacent 0's.
%t A259091 Table[k = 0; While[! SequenceCount[IntegerDigits[2^k], Flatten[ConstantArray[IntegerDigits[n], 2]]] > 0, k++]; k, {n, 0, 100}] (* _Robert Price_, May 17 2019 *)
%o A259091 (Python)
%o A259091 def A259091(n):
%o A259091     s, k, k2 = str(n)*2, 0, 1
%o A259091     while True:
%o A259091         if s in str(k2):
%o A259091             return k
%o A259091         k += 1
%o A259091         k2 *= 2 # _Chai Wah Wu_, Jun 18 2015
%Y A259091 Cf. A006889, A131535, A131536, A259089, A063565, A259092.
%K A259091 nonn,base
%O A259091 0,1
%A A259091 _N. J. A. Sloane_, Jun 18 2015
%E A259091 More terms from _Chai Wah Wu_, Jun 18 2015