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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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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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.
J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010. See pp. 6, 280.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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.
Index entries for sequences related to 3x+1 (or Collatz) problem
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MAPLE
| ina:= proc(n) evalb(n=1) end:
a:= proc(n) option remember; local k, t;
if n=1 then 1
else for k from a(n-1)+1 while not
(irem(k, 2, 't')=0 and ina(t) or
irem(k, 3, 't')=2 and ina(t) or
irem(k, 6, 't')=3 and ina(t) )
do od: ina(k):= true; k
fi
end:
seq (a(n), n=1..80); # Alois P. Heinz, Mar 16 2011
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MATHEMATICA
| s={1}; Do[a=s[[n]]; s=Union[s, {2a, 3a+2, 6a+3}], {n, 1000}]; s (* Zak Seidov Mar 15 2011 *)
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PROG
| (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
(Haskell)
import Data.Set (Set, fromList, insert, deleteFindMin)
a005658 n = a005658_list !! (n-1)
a005658_list = klarner $ fromList [1, 2] where
klarner :: Set Integer -> [Integer]
klarner s = m : (klarner $
insert (2*m) $ insert (3*m+2) $ insert (6*m+3) s')
where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Mar 14 2011
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CROSSREFS
| Cf. A002977, A185661.
Sequence in context: A069011 A101185 A045702 * A166021 A003714 A010402
Adjacent sequences: A005655 A005656 A005657 * A005659 A005660 A005661
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Oct 16 2000
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