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A014120 Smallest number of persistence n over product-of-nonzero-digits function. 11
0, 10, 25, 39, 77, 679, 6788, 68889, 2677889, 26888999, 3778888999, 267777777889999, 77777777788888888888899999, 37777777777777777777777777778888889999999999999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Comments from Marc Lapierre, Sep 09 2020, updated Mar 06 2021 (Start)

Let a(b) denote a string of b copies of the digit a. For example, 3(5) would represent 33333.

Here are recent discoveries and the initials of the discoverers:

14 2(1)6(1)7(1)8(99)9(10) by WW

15 6(1)7(157)8(46)9(25) by WW

16 3(1)7(54)8(82)9(353) by WW

17 3(1)7(27)8(622)9(399) by WW

18 3(1)7(140)8(258)9(1946) by WW

19 2(1)7(122)8(498)9(4297) by ML

Conjectured terms follow:

20 2(1)7(723)8(211)9(9825) by ML

21 4(1)7(169)8(26)9(23367) by ML

22 2(1)7(569)8(332)9(50594) by ML

23 3(1)7(549)8(133)9(111860) by CC

24 3(1)8(6757)9(241726) by CC

25 3(1)7(641)8(8799)9(536071) by CC

26 2(1)8(20197)9(1179021) by CC

27 6(1)7(33710)8(47842)9(2573440) by CC

28 3(1)7(25023)8(122861)9(5897088) by CC

29 8(227088)9(12815927) by CC

30 2(1)7(7631152)8(11913266)9(10305691) by CC

31 2(1)6(1)7(18206905)8(1955318)9(48704671) by CC

32 7(31286605)8(62583498)9(62593158) by CC

33 6(1)7(68627838)8(137266420)9(137237126) by CC

34 4(1)7(129281566)8(383857095)9(241421333) by CC

35 2(1)8(1798834965)9(5997589) by CC

36 3(1)8(3384640858)9(611297938) by CC

WW=Wilfred Whiteside & Phil Carmody (see link)

ML=Marc Lapierre

CC=Christophe Clavier

It seems a safe conjecture that this sequence is infinite.

(End)

LINKS

Marc Lapierre, Table of n, a(n) for n = 0..16

Marc Lapierre, Multiplicative persistence computation

N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.

Wilfred Whiteside & Phil Carmody, Puzzle 341. Multiplicative persistence, Erdos style, Problems & Puzzles: Puzzles.

CROSSREFS

Cf. A003001.

Sequence in context: A074814 A002600 A087473 * A003001 A198377 A038350

Adjacent sequences:  A014117 A014118 A014119 * A014121 A014122 A014123

KEYWORD

nonn,base,nice,changed

AUTHOR

David W. Wilson

EXTENSIONS

Edited by N. J. A. Sloane, Sep 11 2020 following suggestions from Marc Lapierre, Sep 09 2020

STATUS

approved

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Last modified March 8 08:27 EST 2021. Contains 341942 sequences. (Running on oeis4.)