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%I A302853 #6 Jun 07 2018 22:07:17
%S A302853 0,1,3,2,6,4,12,8,9,11,10,14,30,16,17,19,18,22,20,28,24,25,27,26,31,5,
%T A302853 7,15,13,29,21,23,87,64,65,67,66,70,68,76,72,73,75,74,78,94,80,81,83,
%U A302853 82,86,84,92,88,89,91,90,95,69,71,79,77,93,85,117,32,33,41,40,44,36,52,48,49,57,56,60,124,96,97,105,104,108,100,116,112,113,121,120,125
%N A302853 Suspected permutation of nonnegative integers: a(n) = A052331(A282291(1+n)).
%C A302853 Shares with sequences like A003188, A006068, A300838, A302846, A303765, A303767, A304083 and A304533 the property that when moving from any a(n) to a(n+1) either a subset of 0-bits are toggled on (changed to 1's), or a subset of 1-bits are toggled off (changed to 0's), but no both kind of changes may occur at the same step.
%H A302853 Antti Karttunen, Table of n, a(n) for n = 0..30530
%H A302853 Index entries for sequences related to binary expansion of n
%H A302853 Index entries for sequences that are permutations of the natural numbers
%F A302853 a(n) = A052331(A282291(1+n)).
%o A302853 (PARI)
%o A302853 up_to_e = 2^15;
%o A302853 v050376 = vector(up_to_e);
%o A302853 A050376(n) = v050376[n];
%o A302853 ispow2(n) = (n && !bitand(n,n-1));
%o A302853 i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e,break));
%o A302853 A052331(n) = { my(s=0,e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
%o A302853 A302853(n) = A052331(A282291(1+n)); \\ Needs also code from A282291.
%Y A302853 Cf. A302854 (inverse).
%Y A302853 Cf. A052331, A282291.
%Y A302853 Cf. also A304533.
%K A302853 nonn
%O A302853 0,3
%A A302853 _Antti Karttunen_, May 17 2018
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