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A005520
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Smallest number of complexity n: smallest number requiring n 1's to build using + and *.
(Formerly M0523)
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11
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1, 2, 3, 4, 5, 7, 10, 11, 17, 22, 23, 41, 47, 59, 89, 107, 167, 179, 263, 347, 467, 683, 719, 1223, 1438, 1439, 2879, 3767, 4283, 6299, 10079, 11807, 15287, 21599, 33599, 45197, 56039, 81647, 98999, 163259, 203999, 241883, 371447, 540539, 590399, 907199
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Largest number of complexity n is given by A000792. - David W. Wilson (davidwwilson(AT)comcast.net), Oct 03 2005
After 1438 = 2 * 719, all elements through 8206559 are primes. Equivalently, except for a(4) = 4, a(7) = 10, a(10) = 22 and a(25) = 1438, we have a(1) through a(53) are all primes. - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 07 2006
a(54)-a(89) are all primes. - Jānis Iraids (jiraids(AT)inbox.lv), Apr 21 2011
Previous observations (primes with property -1 mod 120) still hold [From Martins Opmanis (askola(AT)latnet.lv), Oct 16 2009]
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, Sec. F26 (related material).
D. A. Rawsthorne, How many 1's are needed?, Fib. Quart. 27 (1989), 14-17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Eric Weisstein's World of Mathematics, Integer Complexity
Janis Iraids, Table of n, a(n) for n = 1..89
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EXAMPLE
| Examples from Piotr Fabian:
1=1, 1 "one": first 1, z(1)=1
2=1+1, 2 "ones": first 2, z(2)=2
3=1+1+1, 3 "ones": first 3, z(3)=3
4=1+1+1+1, 4 "ones": first 4, z(4)=4
5=1+1+1+1+1, 5 "ones": first 5, z(5)=5
6=(1+1)*(1+1+1), 5 "ones"
7=1+((1+1)*(1+1+1)), 6 "ones": first 6, z(6)=7
8=(1+1)*(1+1+1+1), 6 "ones"
9=(1+1+1)*(1+1+1), 6 "ones"
10=1+((1+1+1)*(1+1+1)), 7 "ones": first 7, z(7)=10
11=1+(1+(1+1+1)*(1+1+1)), 8 "ones": first 8, z(8)=11
12=(1+1)*((1+1)*(1+1+1)), 7 "ones"
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PROG
| See the Python program by Tim Peters at A005421.
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CROSSREFS
| Cf. A005245, A025280, A003037.
A005421 [From Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 08 2009]
Sequence in context: A144430 A157082 A133493 * A048183 A122975 A089597
Adjacent sequences: A005517 A005518 A005519 * A005521 A005522 A005523
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by David W. Wilson (davidwwilson(AT)comcast.net) 5/97. Extended to terms a(40)=163259 and a(41)=203999 by John W. Layman (layman(AT)math.vt.edu) 3/11/99. Further terms from Piotr Fabian (PCF(AT)who.net), Mar 30 2001.
Ed Pegg Jr, www.mathpuzzle.com, Apr 10 2001, notes that all the new terms are -1 mod 120.
a(68)-a(89) from Jānis Iraids (jiraids(AT)inbox.lv), Apr 20 2011.
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