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Search: id:A005658
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| A005658 |
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If n appears so do 2n, 3n+2, 6n+3.
(Formerly M0969)
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+0
2
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| 1, 2, 4, 5, 8, 9, 10, 14, 15, 16, 17, 18, 20, 26, 27, 28, 29, 30, 32, 33, 34, 36, 40, 44, 47, 50, 51, 52, 53, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 72, 80, 83, 86, 87, 88, 89, 92, 93, 94, 98, 99, 100, 101, 102, 104, 105, 106, 108, 110, 111, 112, 114, 116, 120, 122, 123
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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David Klarner and coauthors studied several sequences of this type. Some of the references here apply generally to this class of sequences.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. K. Guy, Don't try to solve these problems, Amer. Math. Monthly, 90 (1983), 35-41.
Guy, R. K., Klarner-Rado Sequences. Section E36 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 237, 1994.
Hoffman, D. G. and Klarner, D. A. Sets of integers closed under affine operators-the finite basis theorem. Pacific J. Math. 83 (1979), no. 1, 135-144.
Hoffman, D. G. and Klarner, D. A. Sets of integers closed under affine operators-the closure of finite sets. Pacific J. Math. 78 (1978), no. 2, 337-344.
Klarner, David A., m-Recognizability of sets closed under certain affine functions. Discrete Appl. Math. 21 (1988), no. 3, 207-214.
Klarner, David A. and Post, Karel Some fascinating integer sequences. A collection of contributions in honour of Jack van Lint. Discrete Math. 106/107 (1992), 303-309.
Klarner, D. A. and Rado, R. Arithmetic properties of certain recursively defined sets. Pacific J. Math. 53 (1974), 445-463.
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 1..15889
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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PROGRAM
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(C++) #include <stdio.h> #include <iostream> #include <set> using namespace std ; int main(int argc, char *argv[]) { const int anmax= 40000 ; set<int> a ; a.insert(1) ; for(int i=0; i< anmax ; i++) { if( a.count(i) ) { if( 2*i<=anmax) a.insert(2*i) ; if( 3*i+2 <= anmax) a.insert(3*i+2) ; if( 6*i+3 <= anmax) a.insert(6*i+3) ; } } int n=1 ; for(int i=0; i < anmax; i++) { if( a.count(i) ) { cout << n << " " << i << endl ; n++ ; } } return 0 ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 20 2006
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CROSSREFS
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Sequence in context: A069011 A101185 A045702 this_sequence A166021 A003714 A010402
Adjacent sequences: A005655 A005656 A005657 this_sequence A005659 A005660 A005661
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Oct 16 2000
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