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

1,1

Comments

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

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A051248.

Sequence in context: A341506 A154349 A268068 * A051248 A228615 A267823

Adjacent sequences: A073598 A073599 A073600 * A073602 A073603 A073604

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Aug 04 2002

Status

approved