A176763 - OEIS

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

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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