A176763 Smallest power of 3 whose decimal expansion contains n.

59049, 1, 27, 3, 243, 6561, 6561, 27, 81, 9, 10460353203, 1162261467, 129140163, 31381059609, 177147, 1594323, 129140163, 177147, 2187, 19683, 387420489, 2187, 1162261467, 1594323, 243, 2541865828329, 1162261467, 27, 282429536481, 729, 43046721, 531441, 1594323

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 3 as A030001 is to 2.

Examples

			a(1) = 1 because 3^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 27 because 3^3 = 27 has "2" as a substring.
a(10) = 10460353203 because 3^21 = 10460353203 is the smallest power of 3 whose decimal expansion contains "10" (in this case, "10" happens to be the left-hand or initial digits, but that is not generally true).
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000244, A030000, A030001, A063565, A018856.

Programs

Mathematica

A176763[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[3^++k], IntegerString[n]]]; 3^k]; Array[A176763, 50, 0] (* Paolo Xausa, Apr 03 2024 *)

Python

def a(n):
    k, strn = 0, str(n)
    while strn not in str(3**k): k += 1
    return 3**k
print([a(n) for n in range(33)]) # Michael S. Branicky, Apr 03 2024

Formula

a(n) = MIN{A000244(i) such that n in decimal representation is a substring of A000244(i)}.

Extensions

More terms from Sean A. Irvine and Jon E. Schoenfield, May 05 2010

a(0) prepended by Paolo Xausa, Apr 03 2024