

A163233


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


7



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
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OFFSET

0,3


COMMENTS

The top left 8x8 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 2x2 corner, 2x4 rectangle ((0,1,5,4),(2,3,7,6)) or 4x4 corner one obtains Karnaugh map templates for 2, 3 or 4 variables respectively (although not the standard ones usually given in the textbooks).


LINKS

A. 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))


PROG

(Scheme:) (define (A163233bi x y) (+ (A000695 (A003188 x)) (* 2 (A000695 (A003188 y)))))
(define (A163233 n) (A163233bi (A025581 n) (A002262 n)))


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


AUTHOR

Antti Karttunen, Jul 29 2009


STATUS

approved



