

A073601


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


3



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
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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: A215933 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



