login
This site is supported by donations to The OEIS Foundation.
Logo

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003001 Smallest number of persistence n.
(Formerly M4687)
43
0, 10, 25, 39, 77, 679, 6788, 68889, 2677889, 26888999, 3778888999, 277777788888899 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

Probably finite.

The persistence of a number (A031346) is the number of times you need to multiply the digits together before reaching a single digit.

REFERENCES

Alex Bellos, Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math, Free Press, 2010, page 176.

M. R. Diamond, Multiplicative persistence base 10: some new null results, http://www.markdiamond.com.au/download/joous-3-1-1.pdf.

M. Gardner, Fractal Music, Hypercards and More, Freeman, NY, 1991, pp. 170, 186.

C. A. Pickover, Wonders of Numbers, "Persistence", Chapter 28, Oxford University Press NY 2001.

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 66.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

W. Schneider, The Persistence of a Number

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

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Wikipedia, Persistence of a number

EXAMPLE

E.g. 77 -> 49 -> 36 -> 18 -> 8 has persistence 4.

CROSSREFS

Cf. A031346 (persistence), A133500 (powertrain), A133048 (powerback).

Cf. A006050, A007954, A031286, A031347, A033908, A046511, etc.

Cf. A121105-A121111.

Sequence in context: A002600 A087473 A014120 * A198377 A038350 A003344

Adjacent sequences:  A002998 A002999 A003000 * A003002 A003003 A003004

KEYWORD

nonn,fini,nice,base

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified February 16 03:44 EST 2012. Contains 205860 sequences.