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A002977
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a(1) = 1; subsequent terms are defined by the rule that if m is present so are 2m+1 and 3m+1.
(Formerly M2335)
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18
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1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 39, 40, 43, 45, 46, 55, 57, 58, 63, 64, 67, 79, 81, 82, 85, 87, 91, 93, 94, 111, 115, 117, 118, 121, 127, 129, 130, 135, 136, 139, 159, 163, 165, 166, 171, 172, 175, 183, 187, 189, 190, 193, 202, 223, 231, 235, 237
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internal format)
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OFFSET
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1,2
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COMMENTS
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Complement of A132142: A132138(a(n)) = 1; for all terms m there exists at least one x such that A132140(x)=m. - Reinhard Zumkeller, Aug 20 2007
a(n+1) = A007448(a(n)); giving also the record values of A007448 and their positions. [From Reinhard Zumkeller, Jul 14 2010]
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REFERENCES
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M. L. Fredman and D. E. Knuth, Recurrence relations based on minimization, Abstract 71T-B234, Notices Amer. Math. Soc., 18 (1971), 960.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 78.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
Benoit Cloitre, Illustration of initial terms
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FORMULA
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It seems that limit as n->infinity of log(A002977(n))/log(n) = C = 1.3.. and probably A002977(n) is asymptotic to u*n^C with u=1.0... - Benoit Cloitre, Nov 06 2002
Limit as n->infinity of log(A002977(n))/log(n) = C = 1.269220905243564855888589424556..., and limit as n->infinity of A002977(n)/n^C = u = 1.33... - Yi Yang, Jul 23 2011
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EXAMPLE
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a(10)=21=2*(3*(2*1+1)+1)+1: A132139(A132140(10))=A132139(43)=21;
a(14)=31=3*(3*(2*1+1)+1)+1=2*(2*(2*(2*1+1)+1)+1)+1: A132139(A132140(14))=A132139(52)=31 and A132139(A132140(16))=A132139(121)=31.
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MATHEMATICA
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Union[ Flatten[ NestList[{2# + 1, 3# + 1} &, 1, 6]]] (from Robert G. Wilson v, May 11 2005)
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PROG
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(Haskell)
import Data.Set
a002977 n = a002977_list !! (n-1)
a002977_list = f $ singleton 1 where
f :: Set Integer -> [Integer]
f s = m : (f $ insert (3*m+1) $ insert (2*m+1) s') where
(m, s') = deleteFindMin s
- Reinhard Zumkeller, Feb 10 2011
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CROSSREFS
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Cf. A007448, A058361, A076291, A077477.
Sequence in context: A029739 A005098 A185661 * A024799 A212013 A039579
Adjacent sequences: A002974 A002975 A002976 * A002978 A002979 A002980
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Ray Chandler, Sep 06 2003
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STATUS
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approved
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