%I A014682
%S A014682 0,2,1,5,2,8,3,11,4,14,5,17,6,20,7,23,8,26,9,29,10,32,11,35,12,38,13,
%T A014682 41,14,44,15,47,16,50,17,53,18,56,19,59,20,62,21,65,22,68,23,71,24,
%U A014682 74,25,77,26,80,27,83,28,86,29,89,30,92,31,95,32,98,33,101,34,104
%N A014682 Intertwining of sequence '2,5,8,11,... ("add 3")' and the nonnegative 
               integers.
%C A014682 a(n) = log to the base 2 of A076936(n). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Oct 19 2002
%C A014682 It appears that a(n)=if(mod(n-1,2)=0, (n-1)/2, (3(n-1)+1)/2). - Paul 
               Barry (pbarry(AT)wit.ie), Mar 31 2008
%C A014682 Partial sums are A093353. - Paul Barry (pbarry(AT)wit.ie), Mar 31 2008
%C A014682 Absolute first differences are essentially in A014681 and A103889. - 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 05 2008
%C A014682 a(n)= 5/4 + (1/2)*((-1)^n)*n + (3/4)*(-1)^n + n - Alexander R. Povolotsky 
               (pevnev(AT)juno.com), Apr 05 2008
%F A014682 G.f.: x(2+x+x^2)/(1-x^2)^2; a(n)=(4n+1)/4-(2n+1)(-1)^n/4 [offset 0]. 
               - Paul Barry (pbarry(AT)wit.ie), Mar 31 2008
%F A014682 a(n) = -a(n-1) + a(n-2) + a(n-3) + 4 - John W. Layman (layman(AT)math.vt.edu)
%F A014682 For n > 1 this is the image of n under the modified "3x+1" map (cf. A006370): 
               n -> n/2 if n is even, n -> (3n+1)/2 if n is odd. - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), May 12 2002
%F A014682 O.g.f.: x*(2+x+x^2)/[(-1+x)^2*(1+x)^2]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Apr 05 2008
%p A014682 A076936 := proc(n) option remember ; local apr,ifr,me,i,a ; if n <=2 
               then n^2 ; else apr := mul(A076936(i),i=1..n-1) ; ifr := ifactors(apr)[2] 
               ; me := -1 ; for i from 1 to nops(ifr) do me := max(me, op(2,op(i,
               ifr))) ; od ; me := me+ n-(me mod n) ; a := 1 ; for i from 1 to nops(ifr) 
               do a := a*op(1,op(i,ifr))^(me-op(2,op(i,ifr))) ; od ; if a = A076936(n-1) 
               then me := me+n ; a := 1 ; for i from 1 to nops(ifr) do a := a*op(1,
               op(i,ifr))^(me-op(2,op(i,ifr))) ; od ; fi ; RETURN(a) ; fi ; end: 
               A014682 := proc(n) log[2](A076936(n)) ; end: for n from 1 to 85 do 
               printf("%d, ",A014682(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 20 2007
%Y A014682 Cf. A076936, A076938, A016116.
%Y A014682 Cf. A006370.
%Y A014682 Sequence in context: A152992 A070951 A076937 this_sequence A111361 A167160 
               A082010
%Y A014682 Adjacent sequences: A014679 A014680 A014681 this_sequence A014683 A014684 
               A014685
%K A014682 nonn,easy
%O A014682 1,2
%A A014682 Mohammad K. Azarian (ma3(AT)evansville.edu)
%E A014682 Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 26 2008, at 
               the suggestion of Artur Jasinski (grafix(AT)csl.pl)