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 A324309 Smallest number m such that m is not a multiple of 10 and m^n has two or more identical adjacent decimal digits. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 30 23:40 EST 2023. Contains 367464 sequences. (Running on oeis4.)