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Search: id:A007932
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| A007932 |
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Numbers that contain only 1's, 2's and 3's. |
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+0
6
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| 1, 2, 3, 11, 12, 13, 21, 22, 23, 31, 32, 33, 111, 112, 113, 121, 122, 123, 131, 132, 133, 211, 212, 213, 221, 222, 223, 231, 232, 233, 311, 312, 313, 321, 322, 323, 331, 332, 333, 1111, 1112, 1113, 1121, 1122, 1123, 1131, 1132, 1133, 1211, 1212, 1213, 1221
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence is the alternate number system in base 3. - Robert R. Forslund (forslund(AT)tbaytel.net), Jun 27 2003
a(n) is the "bijective base-k numeration" or "k-adic notation" for k=3. [From Chris Gaconnet (gaconnet(AT)gmail.com), May 27 2009]
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REFERENCES
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K. Atanassov, On the 97-th, 98-th and the 99-th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 3, 89-93.
K. Atanassov, On Some of Smarandache's Problems, American Research Press, 1999, 16-21.
F. Smarandache, Only Problems, not Solutions!, Xiquan Publ., Phoenix-Chicago, 1993.
Robert R. Forslund, A Logical Alternative to the Existing Positional Number System, Southwest Journal of Pure and Applied Mathematics. Vol. 1 1995 pp. 27-29.
James E. Foster, A Number System without a Zero-Symbol, Mathematics Magazine, Vol. 21, No. 1. (1947), pp. 39-41.
A. Salomaa, Formal Languages, Academic Press, 1973. pages 90-91. [From Chris Gaconnet (gaconnet(AT)gmail.com), May 27 2009]
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LINKS
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K. Atanassov, On Some of Smarandache's Problems
Robert R. Forslund, A Logical Alternative to the Existing Positional Number System
F. Smarandache, Only Problems, Not Solutions!.
EMIS, Mirror site for Southwest Journal of Pure and Applied Mathematics
Wikipedia, Bijective numeration [From Chris Gaconnet (gaconnet(AT)gmail.com), May 27 2009]
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MATHEMATICA
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NextNbr[n_] := Block[{d = IntegerDigits[n + 1], l}, l = Length[d]; While[l != 1, If[ d[[l]] > 3, d[[l - 1]]++; d[[l]] = 1]; l-- ]; If[ d[[1]] > 3, d[[1]] = 11]; FromDigits[d]]; NestList[ NextNbr, 1, 51]
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CROSSREFS
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Sequence in context: A083758 A127494 A130803 this_sequence A035122 A085305 A116032
Adjacent sequences: A007929 A007930 A007931 this_sequence A007933 A007934 A007935
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KEYWORD
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nonn,base
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AUTHOR
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R. Muller
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2002
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