A374922 a(n) is the least k such that 3^k begins with n!.

0, 0, 3, 8, 5, 805, 1689, 12317, 197209, 520852, 4493819, 16769097, 2053077332, 1110380591, 39230711849, 516641987008, 62653098988435, 398166000236882, 7896283077809532, 99956735615338266, 5161719458617927763, 63295038588725505792, 659220983938327840981

Offset: 0

Author

Zhining Yang, Jul 23 2024

Keywords

• nonn
• base

Examples

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

Links

• Zhao Hui Du, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A018858, A000142, A374923.

Programs

Mathematica

a[n_] := Module[{target = IntegerDigits[n!], k = 0},
   While[UnsameQ[Take[IntegerDigits[3^k], Length@target], target],
    k++]; k];
Table[a[n], {n, 0, 8}]

Formula

a(n) = A018858(n!).

Extensions

a(13) onwards from Zhao Hui Du, Oct 03 2024