A163233 Two-dimensional Binary Reflected Gray Code: a(i,j) = bits of binary expansion of A003188(i) interleaved with that of A003188(j).

0, 1, 2, 5, 3, 10, 4, 7, 11, 8, 20, 6, 15, 9, 40, 21, 22, 14, 13, 41, 42, 17, 23, 30, 12, 45, 43, 34, 16, 19, 31, 28, 44, 47, 35, 32, 80, 18, 27, 29, 60, 46, 39, 33, 160, 81, 82, 26, 25, 61, 62, 38, 37, 161, 162, 85, 83, 90, 24, 57, 63, 54, 36, 165, 163, 170, 84, 87, 91

Offset

0,3

Comments

The top left 8 X 8 corner of the array is

+0 +1 +5 +4 20 21 17 16

+2 +3 +7 +6 22 23 19 18

10 11 15 14 30 31 27 26

+8 +9 13 12 28 29 25 24

40 41 45 44 60 61 57 56

42 43 47 46 62 63 59 58

34 35 39 38 54 55 51 50

32 33 37 36 52 53 49 48

By taking the top left 2 X 2 corner, 2 X 4 rectangle ((0,1,5,4),(2,3,7,6)) or 4 X 4 corner one obtains Karnaugh map templates for 2, 3 or 4 variables respectively (although not the standard ones usually given in the textbooks).

Links

Antti Karttunen, Table of n, a(n) for n = 0..2079

Wikipedia, Karnaugh map

Index entries for sequences that are permutations of the natural numbers

Formula

a(x,y) = A000695(A003188(x)) + 2*A000695(A003188(y)).

Mathematica

Table[Function[k, FromDigits[#, 2] &@ Apply[Function[{a, b}, Riffle @@ Map[PadLeft[#, Max[Length /@ {a, b}]] &, {a, b}]], Map[IntegerDigits[#, 2] &@ BitXor[#, Floor[#/2]] &, {k, j}]]][i - j], {i, 0, 11}, {j, i, 0, -1}] // Flatten (* Michael De Vlieger, Jun 25 2017 *)

Prog

(Scheme:) (define (A163233bi x y) (+ (A000695 (A003188 x)) (* 2 (A000695 (A003188 y)))))
(define (A163233 n) (A163233bi (A025581 n) (A002262 n)))
(Python)
def a000695(n):
    n=bin(n)[2:]
    x=len(n)
    return sum([int(n[i])*4**(x - 1 - i) for i in range(x)])
def a003188(n): return n^(n>>1)
def a(n, k): return a000695(a003188(n)) + 2*a000695(a003188(k))
for n in range(21): print([a(n - k, k) for k in range(n + 1)]) # Indranil Ghosh, Jun 25 2017

Crossrefs

Inverse: A163234. a(n) = A057300(A163235(n)). Transpose: A163235. Row sums: A163242. Cf. A054238, A147995.

Sequence in context: A044043 A133128 A057337 * A096666 A191855 A064664

Adjacent sequences: A163230 A163231 A163232 * A163234 A163235 A163236

Keyword

nonn,tabl,look

Author

Antti Karttunen, Jul 29 2009

Status

approved