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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 Nov 01 2020 (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

Conjectured terms follow:

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

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

19 6(1)7(184)8(630)9(4181) by ML

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)6(1)7(963)8(559)9(50115) by ML

23 3(1)7(384)8(212)9(113666) by ML

24 3(1)7(31)8(18805)9(233233) by ML

25 2(1)6(1)7(268)8(6)9(556726) by RC

26 2(1)7(115)8(53)9(1224832) by RC

27 3(1)8(587926)9(2310776) by JC

28 9(6202648) by JC

29 9(13282730) by RC

30 9(32908293) by ML

31 3(1)7(10983476)8(15120761)9(49810746) by JC

32 9(183369477) by ML

33 7(543003300) by ML

34 9(801762677) by ML

WW=Wilfred Whiteside & Phil Carmody (see link)

JC=Julien Courties & Maƫl Courtain

ML=Marc Lapierre

RC=Ray Chandler

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

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 December 3 12:20 EST 2020. Contains 338902 sequences. (Running on oeis4.)