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A064869 The minimal number which has multiplicative persistence 5 in base n.

%I A064869 #23 Mar 08 2025 11:07:04
%S A064869 244140624,3629,1601,1535,394,679,317,1099,127,135,582,187,168,157,
%T A064869 201,159,230,215,180,185,246,181,188,195,198,323,239,255,259,267,239,
%U A064869 287,295,293,310,313,280,377,375,395,347,360,321,370,439,431,458,355,362
%N A064869 The minimal number which has multiplicative persistence 5 in base n.
%C A064869 The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(3) and a(4) seem not to exist.
%H A064869 Michael De Vlieger, <a href="/A064869/b064869.txt">Table of n, a(n) for n = 5..10000</a>
%H A064869 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 A064869 Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/persistence.html">Persistence in different bases</a>
%H A064869 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 A064869 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_022.htm">Puzzle 22. Primes and Persistence</a>, The Prime Puzzles and Problems Connection.
%H A064869 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 A064869 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%H A064869 <a href="/index/Rec#order_121">Index entries for linear recurrences with constant coefficients</a>, order 121.
%F A064869 a(n) = 6*n-floor(n/120) for n > 119.
%e A064869 a(9)=394 because 394=[477]->[237]->[46]->[26]->[13]->[3] and no smaller n has persistence 5 in base 9.
%Y A064869 Cf. A003001, A031346, A064867, A064868, A064870, A064871, A064872.
%K A064869 base,easy,nonn
%O A064869 5,1
%A A064869 _Sascha Kurz_, Oct 09 2001