A324309 Smallest number m such that m is not a multiple of 10 and m^n has two or more identical adjacent decimal digits.

11, 12, 11, 16, 6, 6, 6, 4, 4, 6, 3, 3, 4, 7, 7, 2, 6, 2, 2, 3, 4, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2

Offset

1,1

Comments

Least number m such that m is not a multiple of 10 and m^n is a term of A171901.

a(n) >= 2 and a(n) exists for all n > 0, since for sufficiently large k, floor(10^(k/n))^n = 99.... and has 2 adjacent digits 9.

Conjecture: a(n) = 2 for n > 126, i.e., 2^n has two or more identical adjacent decimal digits for n > 126.

Links

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

Example

a(4) = 16 since 16^4 = 65535 has a double digit 5, where i^4 does not have a double digit for i < 16.

Prog

(Python)
def A324309(n):
    m, k = 2, 2**n
    while True:
        s = str(k)
        for i in range(1, len(s)):
            if s[i] == s[i-1]:
                return m
        m += 1
        if m % 10 == 0:
            m += 1
        k = m**n

Crossrefs

Cf. A171901, A217157.

Sequence in context: A352389 A020510 A291521 * A270036 A178405 A162903

Adjacent sequences: A324306 A324307 A324308 * A324310 A324311 A324312

Keyword

nonn,base

Author

Chai Wah Wu, Feb 21 2019

Status

approved