A374922 - OEIS

%I #41 Oct 30 2024 21:06:41

%S 0,0,3,8,5,805,1689,12317,197209,520852,4493819,16769097,2053077332,

%T 1110380591,39230711849,516641987008,62653098988435,398166000236882,

%U 7896283077809532,99956735615338266,5161719458617927763,63295038588725505792,659220983938327840981

%N a(n) is the least k such that 3^k begins with n!.

%H Zhao Hui Du, <a href="/A374922/b374922.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = A018858(n!).

%e a(4) = 5 because 3^5 = 243 is the smallest power of 3 beginning with 4! = 24.

%t a[n_] := Module[{target = IntegerDigits[n!], k = 0},

%t    While[UnsameQ[Take[IntegerDigits[3^k], Length@target], target],

%t     k++]; k];

%t Table[a[n], {n, 0, 8}]

%Y Cf. A018858, A000142, A374923.

%K nonn,base

%O 0,3

%A _Zhining Yang_, Jul 23 2024

%E a(13) onwards from _Zhao Hui Du_, Oct 03 2024