A302782 Inverse permutation to A302781.

0, 1, 3, 15, 5, 2, 21, 14, 63, 6, 255, 12, 85, 20, 4, 341, 1023, 62, 4095, 10, 22, 254, 1365, 13, 5461, 86, 60, 16, 16383, 7, 65535, 340, 252, 1022, 26, 48, 21845, 4094, 84, 9, 87381, 23, 262143, 240, 58, 1366, 1048575, 342, 349525, 5460, 1020, 90, 1398101, 61, 250, 19, 4092, 16382, 4194303, 11, 16777215, 65534, 42

Offset: 1

Author

Antti Karttunen, Apr 14 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A302781 (inverse).

Cf. A006068, A052331, A163355, A302845.

Programs

PARI

up_to = 8192;
v050376 = vector(up_to);
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to,break));
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); };
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
A057300(n) = { my(t=1,s=0); while(n>0, if(1==(n%4),n++,if(2==(n%4),n--)); s += (n%4)*t; n >>= 2; t <<= 2); (s); };
A163355(n) = if(!n,n,my(i = (#binary(n)-1)\2, f = 4^i, d = (n\f)%4, r = (n%f)); if(((1==d)&&!(i%2))||((2==d)&&(i%2)), f+A163355(A057300(r)), if(3==d,f+f+A163355(A057300(r)), (3*f)+A163355(f-1-r))));
A302845(n) = A163355(A006068(A006068(n)));
A302782(n) = A302845(A052331(n));

Formula

a(n) = A302845(A052331(n)).