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

0,3

Links

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

Formula

a(n) = A018858(n!).

Example

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

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}]

Crossrefs

Cf. A018858, A000142, A374923.

Sequence in context: A054792 A144872 A090347 * A268159 A016624 A021263

Adjacent sequences: A374919 A374920 A374921 * A374923 A374924 A374925

Keyword

nonn,base

Author

Zhining Yang, Jul 23 2024

Extensions

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

Status

approved