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A014120 Smallest number of persistence n over product-of-nonzero-digits function. 13
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 May 31 2021: (Start)
Let d(b) denote a string of b copies of the digit d. 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 2(1)6(1)7(822)8(29)9(22601) by CC
22 2(1)7(325)8(1678)9(49461) by CC
23 3(1)7(549)8(133)9(111860) by CC
24 4(1)7(21)8(578)9(244760) by CC
25 2(1)7(309)8(197)9(541758) by CC
26 7(103)8(63)9(1193904) by CC
27 8(3954)9(2613303) by CC
28 6(1)7(6158)8(27383)9(5778277) by CC
29 3(1)5(422)7(117)9(12880950) by CC
30 5(45)7(71)9(29141710) by CC
31 5(216)7(120)9(65374726) by CC
32 5(63)7(24)9(146530307) by CC
33 2(1)8(4597591)9(319806836) by CC
34 6(1)8(9368512)9(719406330) by CC
35 2(1)6(1)8(555702)9(1553958443) by CC
36 3(1)8(3384640858)9(611297938) by CC
37 2(1)6(1)7(1902533551)8(3805122026)9(3805104056) by CC
38 4(1)8(1344555)9(19936453619) 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
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
KEYWORD
nonn,base,nice
AUTHOR
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 April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)