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A064872 The minimal number which has multiplicative persistence 8 in base n.

%I A064872 #17 Mar 08 2025 11:10:12
%S A064872 7577,130883,596667,3644381,2820,61773,2752,5136,7452,38631,2780,8015,
%T A064872 2996,542,8611,4591,575,10586,2532,2681,2764,1016,4547,10151,1065,983,
%U A064872 813,5431,900,1255,983,5179,5117,1190,982,1129,1501,1491,1471,1084
%N A064872 The minimal number which has multiplicative persistence 8 in base n.
%C A064872 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.
%H A064872 M. R. Diamond and D. D. Reidpath, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/PERSIST.PDF">A counterexample to a conjecture of Sloane and Erdos</a>, J. Recreational Math., 1998 29(2), 89-92.
%H A064872 Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/persistence.html">Persistence in different bases</a>
%H A064872 T. Lamont-Smith, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Lamont/lamont5.html">Multiplicative Persistence and Absolute Multiplicative Persistence</a>, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
%H A064872 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_022.htm">Minimal prime with persistence p</a>
%H A064872 N. J. A. Sloane, <a href="http://neilsloane.com/doc/persistence.html">The persistence of a number</a>, J. Recreational Math., 6 (1973), 97-98.
%H A064872 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%H A064872 <a href="/index/Rec#order_40321">Index entries for linear recurrences with constant coefficients</a>, order 40321.
%F A064872 a(n) = 9*n-[n/40320] for n > 40319.
%e A064872 a(13) = 7577 because 7577 is the fewest number with persistence 8 in base 13.
%Y A064872 Cf. A003001, A031346, A064867, A064868, A064869, A064870, A064871.
%K A064872 base,easy,nonn
%O A064872 13,1
%A A064872 _Sascha Kurz_, Oct 08 2001