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A064870 The minimal number which has multiplicative persistence 6 in base n.

%I A064870 #18 Mar 08 2025 11:08:13
%S A064870 11262,57596799,30536,6788,4684,1571,439,667,1964,683,218,857,264,278,
%T A064870 353,393,227,382,344,311,319,307,283,417,422,381,485,436,349,431,436,
%U A064870 449,421,469,327,575,598,483,539,413,511,517,534,641,611,609,476,479
%N A064870 The minimal number which has multiplicative persistence 6 in base n.
%C A064870 The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(5)=1811981201171874, a(6) seems not to exist.
%H A064870 Michael De Vlieger, <a href="/A064870/b064870.txt">Table of n, a(n) for n = 7..10000</a>
%H A064870 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 A064870 Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/persistence.html">Persistence in different bases</a>
%H A064870 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 A064870 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_022.htm">Minimal prime with persistence p</a>
%H A064870 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 A064870 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%H A064870 <a href="/index/Rec#order_721">Index entries for linear recurrences with constant coefficients</a>, order 721.
%F A064870 a(n) = 7*n-[n/720] for n > 719.
%e A064870 a(13) = 439 because 439 = [2'7'10]->[10'10]->[7'9]->[4'11]->[3'5]->[1'2]->[2] needs 6 steps and no fewer n.
%Y A064870 Cf. A003001, A031346, A064867, A064868, A064869, A064871, A064872.
%K A064870 base,easy,nonn
%O A064870 7,1
%A A064870 _Sascha Kurz_, Oct 08 2001