login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306494 Smallest number m such that n*3^m has 2 or more identical adjacent decimal digits. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A306498 A306499

KEYWORD

nonn,base

AUTHOR

Chai Wah Wu, Feb 19 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)