A163355 -id:A163355 - cp's OEIS frontend

A163917 Permutation A163915 shown in N x N grid.

0, 1, 3, 7, 2, 9, 5, 6, 8, 10, 16, 4, 14, 11, 48, 17, 18, 13, 12, 51, 50, 20, 19, 28, 15, 52, 49, 60, 21, 23, 29, 31, 53, 55, 61, 63, 127, 22, 27, 30, 47, 54, 57, 62, 149, 125, 126, 25, 24, 46, 45, 59, 56, 148, 150, 118, 124, 113, 26, 39, 44, 35, 58, 152, 151, 146, 117

Offset: 0

Antti Karttunen, Sep 19 2009

			The top left 8x8 corner of this array:
+0 +1 +7 +5 16 17 20 21
+3 +2 +6 +4 18 19 23 22
+9 +8 14 13 28 29 27 25
10 11 12 15 31 30 24 26
48 51 52 53 47 46 39 37
50 49 55 54 45 44 36 38
60 61 57 59 35 34 40 41
63 62 56 58 32 33 43 42

Inverse: A163918. a(n) = A163915(A054238(n)) = A163355(A163907(n)) = A163905(A163357(n)). See also A163357, A163907.

A163333 Self-inverse permutation of integers: A163327-conjugate of A163332.

Original entry on oeis.org

0, 7, 2, 3, 4, 5, 6, 1, 8, 69, 64, 71, 66, 67, 68, 63, 70, 65, 18, 25, 20, 21, 22, 23, 24, 19, 26, 29, 34, 27, 32, 31, 30, 35, 28, 33, 44, 37, 42, 41, 40, 39, 38, 43, 36, 47, 52, 45, 50, 49, 48, 53, 46, 51, 54, 61, 56, 57, 58, 59, 60, 55, 62, 15, 10, 17, 12, 13, 14, 9, 16, 11

Offset: 0

Antti Karttunen, Jul 29 2009

nonn

The integers [0,(9^k)-1] are confined to range [0,(9^k)-1].

a(n) = A163327(A163332(A163327(n))). A163334 & A163336 give two variants of the Peano curve in an N x N grid. Cf. also A163355.

A302782 Inverse permutation to A302781.

Original entry on oeis.org

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

Antti Karttunen, Apr 14 2018

nonn

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

Cf. A302781 (inverse).

Cf. A006068, A052331, A163355, A302845.

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));

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

cp's OEIS Frontend

A163917 Permutation A163915 shown in N x N grid.

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A163333 Self-inverse permutation of integers: A163327-conjugate of A163332.

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A302782 Inverse permutation to A302781.

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