A171242 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).

242, 42, 43, 83, 44, 41, 157, 24, 39, 50

Offset: 0

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 06 2009

Keywords

• nonn
• base
• fini
• full
• easy

Examples

			n=0: 2^242 = 7067388259113537318333190002971674063309935587502475832486424805170479104
n=1: 2^42 = 4398046511104
n=2: 2^43 = 8796093022208
n=3: 2^83 = 9671406556917033397649408
n=4: 2^44 = 17592186044416
n=5: 2^41 = 2199023255552
n=6: 2^157 = 182687704666362864775460604089535377456991567872
n=7: 2^24 = 16777216
n=8: 2^39 = 549755813888
n=9: 2^50 = 1125899906842624
		

References

• E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig-Jena-Berlin, 2. Auflage 1982
• Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983

Crossrefs

Cf. A000079, A018802, A171132.

Programs

Mathematica

Table[Module[{k=1},While[SequenceCount[IntegerDigits[2^k],{n,n,n}]<1,k++];k],{n,0,9}] (* Harvey P. Dale, Nov 28 2023 *)

Extensions

Offset corrected by Alois P. Heinz, Nov 28 2023