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

0,1

Comments

This is to 3 as A030001 is to 2.

Links

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

Formula

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A343374 A359310 A321826 * A176769 A255893 A046323

Adjacent sequences: A176760 A176761 A176762 * A176764 A176765 A176766

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Apr 25 2010

Extensions

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

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

Status

approved