Search: id:A016945 Results 1-1 of 1 results found. %I A016945 %S A016945 3,9,15,21,27,33,39,45,51,57,63,69,75,81,87,93,99,105,111, %T A016945 117,123,129,135,141,147,153,159,165,171,177,183,189,195, %U A016945 201,207,213,219,225,231,237,243,249,255,261,267,273,279 %N A016945 6n+3. %C A016945 Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 37 ). %C A016945 Continued fraction expansion of tanh(1/3). %C A016945 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 %C A016945 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 %C A016945 A008615(a(n)) = n. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 27 2008 %C A016945 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 %C A016945 A157176(a(n)) = A103333(n+1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009] %C A016945 Contribution from L Pearson (loren.pearson(AT)gmail.com), Jul 02 2009: (Start) %C A016945 Values of n in 2^n-1 that produce a composite with 7 as a factor. %C A016945 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. %C A016945 Other odd n appear to be unrelated prime or semi-prime composites. %C A016945 (End) %D A016945 Friedrich L. Bauer, 'Der (ungerade) Collatz-Baum', Informatik Spektrum 31 (Springer, April 2008). %H A016945 Milan Janjic, Two Enumerative Functions %H A016945 Tanya Khovanova, Recursive Sequences %H A016945 William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N)) %H A016945 William A. Stein, The modular forms database %H A016945 Eric Weisstein's World of Mathematics, Collatz Problem %H A016945 Index entries for sequences related to 3x+1 (or Collatz) problem %F A016945 a(n) = 3(2n+1) = 3*A005408(n), odd multiples of 3. %p A016945 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 %t A016945 a[n_]:=6*n+3;...and/or...Array[3+#*6&,5!,0] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 21 2008] %t A016945 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] %o A016945 (Other) sage: [i+3 for i in range(280) if gcd(i,6) == 6] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009] %o A016945 (Other) sage: [crt(3, n, 3, 5) for n in xrange(3, 50)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2009] %Y A016945 Third row of A092260. %Y A016945 Cf. A008588, A016921, A016933, A016957, A016969. %Y A016945 Subsequence of A061641; complement of A047263. %Y A016945 A000225 [From L Pearson (loren.pearson(AT)gmail.com), Jul 02 2009] %Y A016945 Sequence in context: A029506 A030594 A032676 this_sequence A110108 A162843 A102954 %Y A016945 Adjacent sequences: A016942 A016943 A016944 this_sequence A016946 A016947 A016948 %K A016945 nonn,easy %O A016945 0,1 %A A016945 N. J. A. Sloane (njas(AT)research.att.com). Search completed in 0.002 seconds