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A064872
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The minimal number which has multiplicative persistence 8 in base n.
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8
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7577, 130883, 596667, 3644381, 2820, 61773, 2752, 5136, 7452, 38631, 2780, 8015, 2996, 542, 8611, 4591, 575, 10586, 2532, 2681, 2764, 1016, 4547, 10151, 1065, 983, 813, 5431, 900, 1255, 983, 5179, 5117, 1190, 982, 1129, 1501, 1491, 1471, 1084
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OFFSET
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13,1
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COMMENTS
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The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(7)=1086400325525346, a(10)=2677889, a(11)=757074, a(8) and a(9) seem not to exist.
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LINKS
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Table of n, a(n) for n=13..52.
M. R. Diamond and D. D. Reidpath, A counterexample to a conjecture of Sloane and Erdos, J. Recreational Math., 1998 29(2), 89-92.
Sascha Kurz, Persistence in different bases
T. Lamont-Smith, Multiplicative Persistence and Absolute Multiplicative Persistence, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
C. Rivera, Minimal prime with persistence p
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Multiplicative Persistence
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FORMULA
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a(n) = 9*n-[n/40320] for n > 40319.
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EXAMPLE
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a(13) = 7577 because 7577 is the fewest number with persistence 8 in base 13.
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CROSSREFS
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Cf. A003001, A031346, A064867, A064868, A064869, A064870, A064871.
Sequence in context: A206672 A205516 A260036 * A254909 A254902 A257204
Adjacent sequences: A064869 A064870 A064871 * A064873 A064874 A064875
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KEYWORD
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base,easy,nonn
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AUTHOR
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Sascha Kurz, Oct 08 2001
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STATUS
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approved
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