%I A005941 M0510
%S A005941 1,2,3,4,5,6,9,8,7,10,17,12,33,18,11,16,65,14,129,20,19,34,257,24,13,66,
%T A005941 15,36,513,22,1025,32,35,130,21,28,2049,258,67,40,4097,38,8193,68,23,
%U A005941 514,16385,48,25,26,131,132,32769,30,37,72,259,1026,65537,44,2050,39,64
%N A005941 Inverse of the Doudna sequence A005940.
%C A005941 a(2^k)=2^k. - Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2005
%C A005941 Fixed points: A029747. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 23 2006
%D A005941 J. H. Conway, personal communication.
%D A005941 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005941 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A005941 a(n) = h(g(n,1,1), 0) / 2 + 1 with h(n, m) = if n=0 then m else h(floor(n/
               2), 2*m + n mod 2) and g(n, i, x) = if n=1 then x else (if n mod 
               prime(i) = 0 then g(n/prime(i), i, 2*x+1) else g(n, i+1, 2*x). - 
               Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 23 2006
%t A005941 f[n_] := Block[{p = Partition[ Split[ Join[ IntegerDigits[n - 1, 2], 
               {2}]], 2]}, Times @@ Flatten[ Table[q = Take[p, -i]; Prime[ Count[ 
               Flatten[q], 0] + 1]^q[[1, 1]], {i, Length[p]}] ]]; t = Table[ f[n], 
               {n, 10^5}]; Flatten[ Table[ Position[t, n, 1, 1], {n, 64}]] (from 
               Robert G. Wilson v Feb 22 2005)
%Y A005941 Cf. A103969. Inverse of A005940.
%Y A005941 Sequence in context: A055170 A068384 A005940 this_sequence A075164 A023841 
               A103681
%Y A005941 Adjacent sequences: A005938 A005939 A005940 this_sequence A005942 A005943 
               A005944
%K A005941 nonn
%O A005941 1,2
%A A005941 N. J. A. Sloane (njas(AT)research.att.com).
%E A005941 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2005