A374923 a(n) is the least k such that 2^k begins with n!.

0, 0, 1, 6, 81, 80, 56, 7284, 33889, 2044921, 8151937, 127668791, 258943304, 19207561921, 189815680859, 2687562198191, 75909586168557, 512148453482307, 5376323935222903, 502774568129731130, 1053338431686717460, 122114339415457901831, 2120280158164651048122

Offset: 0

Author

Zhining Yang, Jul 23 2024

Keywords

• nonn
• base

Examples

			a(4) = 81 because 2^81 = 2417851639229258349412352 is the smallest power of 2 beginning with 4! = 24.
		

Links

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

Crossrefs

Cf. A018856, A000142, A152561, A374922.

Programs

Mathematica

a[n_] := Module[{target = IntegerDigits[n!], k = 0},
   While[UnsameQ[Take[IntegerDigits[2^k], Length@target], target],
    k++]; k];
Table[a[n], {n, 0, 8}]

Formula

a(n) = A018856(n!).

Extensions

a(13) onwards from Zhao Hui Du, Oct 02 2024