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A014120 Smallest number of persistence n over product-of-nonzero-digits function.

%I A014120 #99 Feb 19 2025 15:03:33
%S A014120 0,10,25,39,77,679,6788,68889,2677889,26888999,3778888999,
%T A014120 267777777889999,77777777788888888888899999,
%U A014120 37777777777777777777777777778888889999999999999999999
%N A014120 Smallest number of persistence n over product-of-nonzero-digits function.
%C A014120 Comments from _Marc Lapierre_, Sep 09 2020, updated Feb 19 2025: (Start)
%C A014120 Let d(b) denote a string of b copies of the digit d. For example, 3(5) would represent 33333.
%C A014120 Here are recent discoveries and the initials of the discoverers:
%C A014120 14 2(1)6(1)7(1)8(99)9(10) by WW
%C A014120 15 6(1)7(157)8(46)9(25) by WW
%C A014120 16 3(1)7(54)8(82)9(353) by WW
%C A014120 17 3(1)7(27)8(622)9(399) by WW
%C A014120 18 3(1)7(140)8(258)9(1946) by WW
%C A014120 19 2(1)7(122)8(498)9(4297) by ML
%C A014120 20 2(1)7(723)8(211)9(9825) by ML
%C A014120 Conjectured terms follow:
%C A014120 21 2(1)6(1)7(822)8(29)9(22601) by CC
%C A014120 22 2(1)7(325)8(1678)9(49461) by CC
%C A014120 23 2(1)7(1199)8(662)9(110077) by CC
%C A014120 24 7(1335)8(1609)9(241857) by CC
%C A014120 25 4(1)7(155)8(1135)9(540199) by CC
%C A014120 26 6(1)7(124)8(762)9(1192494) by CC
%C A014120 27 4(1)7(94)8(583)9(2616367) by CC
%C A014120 28 3(1)5(6)9(5788986) by CC
%C A014120 29 7(20)8(24)9(12878515) by CC
%C A014120 30 8(67)9(29136478) by CC
%C A014120 31 7(9)8(17)9(64768493) by CC
%C A014120 32 6(1)7(8)8(5)9(144417969) by CC
%C A014120 33 6(1)7(2)8(8)9(324379548) by CC
%C A014120 34 2(1)6(1)7(1)8(31)9(728759871) by CC
%C A014120 35 2(1)6(1)8(555702)9(1553958443) by CC
%C A014120 36 3(1)8(10311016)9(3652133953) by CC
%C A014120 37 2(1)6(1)8(1482224)9(9136624827) by CC
%C A014120 38 3(1)8(1469099)9(19262606200) by CC
%C A014120 39 8(30408394)9(42905304588) by CC
%C A014120 WW=Wilfred Whiteside & Phil Carmody (see link)
%C A014120 ML=Marc Lapierre
%C A014120 CC=Christophe Clavier
%C A014120 It seems a safe conjecture that this sequence is infinite.
%C A014120 (End)
%H A014120 Marc Lapierre, <a href="/A014120/b014120.txt">Table of n, a(n) for n = 0..16</a>
%H A014120 Marc Lapierre, <a href="http://www.ahonga.fr/js/pls430-nostat.html?view=1">Multiplicative persistence computation</a>
%H A014120 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 A014120 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 A014120 Cf. A003001.
%K A014120 nonn,base,nice
%O A014120 0,2
%A A014120 _David W. Wilson_
%E A014120 Edited by _N. J. A. Sloane_, Sep 11 2020 following suggestions from _Marc Lapierre_, Sep 09 2020