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 A116640 a(n) = A116623(A059893(n)). 6
 1, 5, 7, 19, 11, 23, 29, 65, 19, 31, 37, 73, 49, 85, 103, 211, 35, 47, 53, 89, 65, 101, 119, 227, 89, 125, 143, 251, 179, 287, 341, 665, 67, 79, 85, 121, 97, 133, 151, 259, 121, 157, 175, 283, 211, 319, 373, 697, 169, 205, 223, 331, 259, 367, 421, 745, 331 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Viewed as a binary tree, this is (1); 5; 7,19; 11,23,29,65; ... Cf. A116623. If we treat (2n+1) as a binary number with the nonzero bits numbered (highest bit first) from 0..k and the regular binary place value of each nonzero bit numbered from b(0) to b(k) then a(n) = 3^0 * b(0) + 3^1 * b(1) + .. + 3^k. For instance, if n=6 then 2n+1 = 13, which is equal to 8+4+1 or 1101 base(2); and a(n)=29 which is 8*1 + 4*3 + 1*9. - Joe Slater, Jan 23 2016 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Index entries for sequences related to 3x+1 (or Collatz) problem FORMULA a(A000225(n)) = A001047(n+1). For n>= 1 a(A000079(n)) = A062709(n+1). From Joe Slater, Jan 19 2016: (Start) a(0) = 1, a(n) = 3*a(floor(n/2)) - 2*a(floor(n/4)) for n=0 (mod 4) and n>0, a(n) = 6*a(floor(n/4)) - a(floor(n/2)) for n=1 (mod 4), a(n) = a(floor(n/2)) + 2*a(floor(n/4)) for n=2 (mod 4), a(n) = 5*a(floor(n/2)) - 6*a(floor(n/4)) for n=3 (mod 4) (End) a(0) = 1, a(n) = 2*a(floor(n/2)) - A033999(n) * A048883(n) for n>0. - Joe Slater, Jan 22 2016 MAPLE a:= proc(n) option remember; piecewise( n mod 4 = 0, 3*procname(n/2) - 2*procname(n/4), n mod 4 = 1, 6*procname((n-1)/4) - procname((n-1)/2), n mod 4 = 2, procname(n/2) + 2*procname((n-2)/4), 5*procname((n-1)/2) - 6*procname((n-3)/4)) end proc: a(0):= 1: map(a, [\$0..100]); # Robert Israel, Jan 19 2016 MATHEMATICA a[n_] := a[n] = Switch[Mod[n, 4], 0, 3a[Floor[n/2]] - 2a[Floor[n/4]], 1, 6a[Floor[n/4]] - a[Floor[n/2]], 2, a[Floor[n/2]] + 2a[Floor[n/4]], 3, 5a[Floor[n/2]] - 6a[Floor[n/4]]]; a[0]=1; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 28 2016 *) PROG (PARI) a(n) = if(n==0, return(1)); 2*a(n\2) - (-1)^n * 3^hammingweight(n) \\ Charles R Greathouse IV, Jan 21 2016 (PARI) a(n) = my(p=2*n+1, v=vecextract(vector(#binary(p), j, 2^(j-1)), p)); sum(i=0, #v-1, 3^i*v[#v-i]) \\ Joe Slater, May 09 2017 CROSSREFS Cf. A000079, A000225, A001047, A062709. Sequence in context: A297937 A337349 A028319 * A116623 A349170 A046151 Adjacent sequences: A116637 A116638 A116639 * A116641 A116642 A116643 KEYWORD nonn,base,tabf AUTHOR Antti Karttunen, Feb 20 2006. Proposed by Pierre Lamothe (plamothe(AT)aei.ca), May 21 2004. STATUS approved

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Last modified September 26 15:44 EDT 2023. Contains 365660 sequences. (Running on oeis4.)