A306494 Smallest number m such that n*3^m has 2 or more identical adjacent decimal digits.

11, 8, 10, 8, 11, 7, 9, 5, 9, 11, 0, 7, 2, 4, 10, 2, 4, 6, 7, 8, 8, 0, 5, 4, 2, 9, 8, 4, 6, 10, 4, 2, 0, 8, 6, 6, 1, 1, 1, 8, 3, 3, 3, 0, 9, 5, 5, 1, 2, 11, 3, 7, 2, 5, 0, 7, 6, 2, 1, 7, 6, 2, 7, 5, 3, 0, 6, 4, 4, 9, 7, 3, 5, 1, 1, 1, 0, 8, 2, 5, 7, 3, 3, 3, 1

Offset

1,1

Comments

a(n) is smallest m such that 3^m*n is in the sequence A171901 (or -1 if no such m exists).

0 <= a(n) <= 35 for all n > 0. This is proved by showing that for each 0 < n < 10^9, there is a number m <= 35 such that 3^m*n mod 10^9 has adjacent identical digits. If n > 0 and n == 0 mod 10^9, then clearly a(n) = 0.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(A171901(n)) = 0.

Example

a(1) = 11 since 3^11 = 177147 has 2 adjacent digits '7' and no smaller power of 3 has adjacent identical digits.
Record values:
a(1) = 11
a(241) = 12
a(2392) = 14
a(35698) = 15
a(267345) = 16
a(893521) = 17
a(29831625) = 18
a(3232453125) = 19

Prog

(Python)
def A306494(n):
    m, k= 0, n
    while True:
        s = str(k)
        for i in range(1, len(s)):
            if s[i] == s[i-1]:
                return m
        m += 1
        k *= 3

Crossrefs

Cf. A171901, A306305.

Sequence in context: A003567 A085688 A164059 * A068974 A244447 A206420

Adjacent sequences: A306491 A306492 A306493 * A306495 A306496 A306497

Keyword

nonn,base

Author

Chai Wah Wu, Feb 19 2019

Status

approved