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%I #10 Nov 28 2023 19:16:37
%S 242,42,43,83,44,41,157,24,39,50
%N a(n) = k is the smallest exponent k such that at least 3 equal decimal digits "n n n" appear in the decimal representation of 2^k (n=0,1,...,9).
%D E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig-Jena-Berlin, 2. Auflage 1982
%D Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983
%e n=0: 2^242 = 7067388259113537318333190002971674063309935587502475832486424805170479104
%e n=1: 2^42 = 4398046511104
%e n=2: 2^43 = 8796093022208
%e n=3: 2^83 = 9671406556917033397649408
%e n=4: 2^44 = 17592186044416
%e n=5: 2^41 = 2199023255552
%e n=6: 2^157 = 182687704666362864775460604089535377456991567872
%e n=7: 2^24 = 16777216
%e n=8: 2^39 = 549755813888
%e n=9: 2^50 = 1125899906842624
%t Table[Module[{k=1},While[SequenceCount[IntegerDigits[2^k],{n,n,n}]<1,k++];k],{n,0,9}] (* _Harvey P. Dale_, Nov 28 2023 *)
%Y Cf. A000079, A018802, A171132.
%K nonn,base,fini,full,easy
%O 0,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 06 2009
%E Offset corrected by _Alois P. Heinz_, Nov 28 2023
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