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9^a(n) is smallest power of 9 beginning with n.
3

%I #12 Dec 09 2021 06:04:55

%S 0,12,9,7,5,4,3,2,1,21,42,20,19,40,18,17,60,16,59,15,80,14,101,57,13,

%T 78,34,12,77,33,11,98,54,10,119,75,53,9,118,96,52,30,8,95,73,51,7,138,

%U 94,72,50,28,6,115,93,71,49,27,5,114,92,70,48,26,4,135,113,91,69,47,25,3,134

%N 9^a(n) is smallest power of 9 beginning with n.

%H D. Mondot, <a href="/A018870/b018870.txt">Table of n, a(n) for n = 1..32699</a>

%e a(2) = 12 since 9^12 = 282429536481 is the smallest power of 9 that begins with 2.

%o (Python)

%o def a(n):

%o s, k = str(n), 0

%o while not str(9**k).startswith(s): k += 1

%o return k

%o print([a(n) for n in range(1, 74)]) # _Michael S. Branicky_, Dec 09 2021

%Y Cf. A001019, A018869.

%K nonn,base

%O 1,2

%A _David W. Wilson_