0,1

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

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 19 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 semi-prime composites.

(End)

Friedrich L. Bauer, 'Der (ungerade) Collatz-Baum', Informatik Spektrum 31 (Springer, April 2008).

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

a(n) = 3(2n+1) = 3*A005408(n), odd multiples of 3.

a[1]:=3:for n from 2 to 100 do a[n]:=a[n-1]+6 od: seq(a[n], n=1..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008

a[n_]:=6*n+3; ...and/or...Array[3+#*6&, 5!, 0] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 21 2008]

f[n_]:=6*n+3; lst={}; Do[a=f[n]; AppendTo[lst, a], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]

(Other) sage: [i+3 for i in range(280) if gcd(i, 6) == 6] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009]

(Other) sage: [crt(3, n, 3, 5) for n in xrange(3, 50)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2009]

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 this_sequence A110108 A162843 A102954

Adjacent sequences: A016942 A016943 A016944 this_sequence A016946 A016947 A016948

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).