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Smallest power of 9 whose decimal expansion contains n.
1

%I #14 Apr 04 2024 04:00:43

%S 59049,1,729,531441,59049,6561,6561,729,81,9,31381059609,

%T 205891132094649,150094635296999121,31381059609,531441,

%U 150094635296999121,16677181699666569,1350851717672992089,2541865828329,8862938119652501095929

%N Smallest power of 9 whose decimal expansion contains n.

%C This is to 9 as A176763 is to 3 and as A030001 is to 2.

%H Paolo Xausa, <a href="/A176769/b176769.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = MIN{A001019(i) such that n in decimal representation is a substring of A001019(i)}.

%F a(n) = 9^A062526(n). - _Michel Marcus_, Sep 30 2014

%e a(1) = 1 because 9^0 = 1 has "1" as a substring (not a proper substring, though).

%e a(2) = 729 because 9^3 = 729 has "2" as a substring.

%e a(3) = 531441 because 9^6 = 531441 has "3" as a substring.

%t A176769[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[9^++k], IntegerString[n]]]; 9^k]; Array[A176769, 50, 0] (* _Paolo Xausa_, Apr 04 2024 *)

%Y Cf. A001018, A030001, A176763, A176764-A176773.

%K base,easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Apr 25 2010

%E More terms from _Sean A. Irvine_ and _Jon E. Schoenfield_, May 05 2010

%E a(0) prepended by _Paolo Xausa_, Apr 04 2024