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

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, 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, 10, 10, 15, 25, 6, 6, 17, 12, 7, 7, 26, 20, 21, 8, 23, 24, 9, 18, 10, 29

Offset: 1

Author

Reinhard Zumkeller, Aug 04 2002

Keywords

• nonn
• base
• look

Comments

A073600(n) = n^a(n);

A000030(n^a(n)) = A000030(n).

Examples

			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.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051248.

Programs

Haskell

a073601 n = 2 + length
   (takeWhile ((a000030 n /=) . a000030) $ iterate (* n) (n^2))
-- Reinhard Zumkeller, Sep 27 2011

Mathematica

fi[n_] := First[IntegerDigits[n]]; Table[k = 2; While[fi[n^k] != fi[n], k++]; k, {n, 78}] (* Jayanta Basu, Jul 02 2013 *)