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A073601 Least k>1 such that n^k and n have equal leading decimal digits.

%I A073601 #15 Jan 27 2014 12:29:32
%S A073601 2,8,18,6,24,10,20,11,22,2,2,2,2,2,6,5,5,4,4,8,20,4,4,9,6,8,8,3,3,18,
%T A073601 48,3,3,3,12,10,8,6,6,6,6,9,20,15,4,4,4,20,14,24,18,8,19,16,5,5,34,18,
%U A073601 10,10,15,25,6,6,17,12,7,7,26,20,21,8,23,24,9,18,10,29
%N A073601 Least k>1 such that n^k and n have equal leading decimal digits.
%C A073601 A073600(n) = n^a(n);
%C A073601 A000030(n^a(n)) = A000030(n).
%H A073601 Reinhard Zumkeller, <a href="/A073601/b073601.txt">Table of n, a(n) for n = 1..10000</a>
%e A073601 a(4)=6, as 4^6=4096=A073600(4) is the least power of 4 with initial digit =4: 4^2=16, 4^3=64, 4^4=256 and 4^5=1024.
%t A073601 fi[n_] := First[IntegerDigits[n]]; Table[k = 2; While[fi[n^k] != fi[n], k++]; k, {n, 78}] (* _Jayanta Basu_, Jul 02 2013 *)
%o A073601 (Haskell)
%o A073601 a073601 n = 2 + length
%o A073601    (takeWhile ((a000030 n /=) . a000030) $ iterate (* n) (n^2))
%o A073601 -- _Reinhard Zumkeller_, Sep 27 2011
%Y A073601 Cf. A051248.
%K A073601 nonn,base,look
%O A073601 1,1
%A A073601 _Reinhard Zumkeller_, Aug 04 2002