A018870 9^a(n) is smallest power of 9 beginning with n.

0, 12, 9, 7, 5, 4, 3, 2, 1, 21, 42, 20, 19, 40, 18, 17, 60, 16, 59, 15, 80, 14, 101, 57, 13, 78, 34, 12, 77, 33, 11, 98, 54, 10, 119, 75, 53, 9, 118, 96, 52, 30, 8, 95, 73, 51, 7, 138, 94, 72, 50, 28, 6, 115, 93, 71, 49, 27, 5, 114, 92, 70, 48, 26, 4, 135, 113, 91, 69, 47, 25, 3, 134

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Examples

			a(2) = 12 since 9^12 = 282429536481 is the smallest power of 9 that begins with 2.
		

Links

• D. Mondot, Table of n, a(n) for n = 1..32699

Crossrefs

Cf. A001019, A018869.

Programs

Python

def a(n):
    s, k = str(n), 0
    while not str(9**k).startswith(s): k += 1
    return k
print([a(n) for n in range(1, 74)]) # Michael S. Branicky, Dec 09 2021