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3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 105, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219, 225, 231, 237, 243, 249, 255, 261, 267, 273, 279, 285, 291, 297, 303, 309, 315, 321, 327
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 37 ).
Continued fraction expansion of tanh(1/3).
If a 2-set Y and a 3-set Z are disjoint subsets of an n-set X then a(n-4) is the number of 3-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
A008615(a(n)) = n. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 27 2008
Leaves of the Odd Collatz-Tree: a(n) has no odd predecessors in all '3x+1' trajectories where it occurs: A139391(2*k+1) <> a(n) for all k; A082286(n)=A006370(a(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 17 2008
A157176(a(n)) = A103333(n+1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]
Contribution from L Pearson (loren.pearson(AT)gmail.com), Jul 02 2009: (Start)
Values of n in 2^n-1 that produce a composite with 7 as a factor.
Their distribution in 2^n-1 sequence equidistant between terms that have multiple factors of 3 (n=6,12,18,24,30,36,... where the number of factors of 3 equals to [number of times 3 divides n] + 1), recognizing that all even n in the 2^n-1 sequence have at least one factor of 3.
Other odd n appear to be unrelated prime or semiprime composites.
(End)
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REFERENCES
| Friedrich L. Bauer, 'Der (ungerade) Collatz-Baum', Informatik Spektrum 31 (Springer, April 2008).
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LINKS
| Milan Janjic, Two Enumerative Functions
Tanya Khovanova, Recursive Sequences
William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))
William A. Stein, The modular forms database
Eric Weisstein's World of Mathematics, Collatz Problem
Index entries for sequences related to 3x+1 (or Collatz) problem
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FORMULA
| a(n) = 3(2n+1) = 3*A005408(n), odd multiples of 3.
a(n)=12*n-a(n-1) (with a(0)=3) [From Vincenzo Librandi, Nov 20 2010]
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MATHEMATICA
| Range[3, 500, 6] (* From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), May 26 2011 *)
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CROSSREFS
| Third row of A092260.
Cf. A008588, A016921, A016933, A016957, A016969.
Subsequence of A061641; complement of A047263.
A000225 [From L Pearson (loren.pearson(AT)gmail.com), Jul 02 2009]
Sequence in context: A029506 A030594 A032676 * A110108 A162843 A102954
Adjacent sequences: A016942 A016943 A016944 * A016946 A016947 A016948
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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