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%I #97 Mar 12 2022 22:42:36
%S 0,10,25,39,77,679,6788,68889,2677889,26888999,3778888999,
%T 267777777889999,77777777788888888888899999,
%U 37777777777777777777777777778888889999999999999999999
%N Smallest number of persistence n over product-of-nonzero-digits function.
%C Comments from _Marc Lapierre_, Sep 09 2020, updated May 31 2021: (Start)
%C Let d(b) denote a string of b copies of the digit d. For example, 3(5) would represent 33333.
%C Here are recent discoveries and the initials of the discoverers:
%C 14 2(1)6(1)7(1)8(99)9(10) by WW
%C 15 6(1)7(157)8(46)9(25) by WW
%C 16 3(1)7(54)8(82)9(353) by WW
%C 17 3(1)7(27)8(622)9(399) by WW
%C 18 3(1)7(140)8(258)9(1946) by WW
%C 19 2(1)7(122)8(498)9(4297) by ML
%C Conjectured terms follow:
%C 20 2(1)7(723)8(211)9(9825) by ML
%C 21 2(1)6(1)7(822)8(29)9(22601) by CC
%C 22 2(1)7(325)8(1678)9(49461) by CC
%C 23 3(1)7(549)8(133)9(111860) by CC
%C 24 4(1)7(21)8(578)9(244760) by CC
%C 25 2(1)7(309)8(197)9(541758) by CC
%C 26 7(103)8(63)9(1193904) by CC
%C 27 8(3954)9(2613303) by CC
%C 28 6(1)7(6158)8(27383)9(5778277) by CC
%C 29 3(1)5(422)7(117)9(12880950) by CC
%C 30 5(45)7(71)9(29141710) by CC
%C 31 5(216)7(120)9(65374726) by CC
%C 32 5(63)7(24)9(146530307) by CC
%C 33 2(1)8(4597591)9(319806836) by CC
%C 34 6(1)8(9368512)9(719406330) by CC
%C 35 2(1)6(1)8(555702)9(1553958443) by CC
%C 36 3(1)8(3384640858)9(611297938) by CC
%C 37 2(1)6(1)7(1902533551)8(3805122026)9(3805104056) by CC
%C 38 4(1)8(1344555)9(19936453619) by CC
%C WW=Wilfred Whiteside & Phil Carmody (see link)
%C ML=Marc Lapierre
%C CC=Christophe Clavier
%C It seems a safe conjecture that this sequence is infinite.
%C (End)
%H Marc Lapierre, <a href="/A014120/b014120.txt">Table of n, a(n) for n = 0..16</a>
%H Marc Lapierre, <a href="http://www.ahonga.fr/js/pls430-nostat.html?view=1">Multiplicative persistence computation</a>
%H 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 Wilfred Whiteside & Phil Carmody, <a href="https://www.primepuzzles.net/puzzles/puzz_341.htm">Puzzle 341. Multiplicative persistence, Erdos style</a>, Problems & Puzzles: Puzzles.
%Y Cf. A003001.
%K nonn,base,nice
%O 0,2
%A _David W. Wilson_
%E Edited by _N. J. A. Sloane_, Sep 11 2020 following suggestions from _Marc Lapierre_, Sep 09 2020
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