A163235 Two-dimensional Binary Reflected Gray Code, transposed version: a(i,j) = bits of binary expansion of A003188(j) interleaved with that of A003188(i).

0, 2, 1, 10, 3, 5, 8, 11, 7, 4, 40, 9, 15, 6, 20, 42, 41, 13, 14, 22, 21, 34, 43, 45, 12, 30, 23, 17, 32, 35, 47, 44, 28, 31, 19, 16, 160, 33, 39, 46, 60, 29, 27, 18, 80, 162, 161, 37, 38, 62, 61, 25, 26, 82, 81, 170, 163, 165, 36, 54, 63, 57, 24, 90, 83, 85, 168, 171, 167

Offset

0,2

Comments

The top left 8x8 corner of this array

+0 +2 10 +8 40 42 34 32

+1 +3 11 +9 41 43 35 33

+5 +7 15 13 45 47 39 37

+4 +6 14 12 44 46 38 36

20 22 30 28 60 62 54 52

21 23 31 29 61 63 55 53

17 19 27 25 57 59 51 49

16 18 26 24 56 58 50 48

corresponds with Adamson's "H-bond codon-anticodon magic square" (see page 287 in Pickover's book):

CCC CCU CUU CUC UUC UUU UCU UCC

CCA CCG CUG CUA UUA UUG UCG UCA

CAA CAG CGG CGA UGA UGG UAG UAA

CAC CAU CGU CGC UGC UGU UAU UAC

AAC AAU AGU AGC GGC GGU GAU GAC

AAA AAG AGG AGA GGA GGG GAG GAA

ACA ACG AUG AUA GUA GUG GCG GCA

ACC ACU AUU AUC GUC GUU GCU GCC

when the base-triples are interpreted as quaternary (base-4) numbers, with the following rules: C = 0, A = 1, U = 2, G = 3.

References

Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002, pp. 285-289.

Links

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

Index entries for sequences that are permutations of the natural numbers

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, 0, i}] // Flatten (* Michael De Vlieger, Jun 25 2017 *)

Prog

(Scheme:) (define (A163235 n) (A163233bi (A002262 n) (A025581 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(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, Jun 25 2017

Crossrefs

Inverse: A163236. a(n) = A057300(A163233(n)). Transpose: A163233. Row sums: A163242. Cf. A054238, A147995.

Sequence in context: A011268 A332080 A225911 * A142963 A099755 A202483

Adjacent sequences: A163232 A163233 A163234 * A163236 A163237 A163238

Keyword

nonn,tabl

Author

Antti Karttunen, Jul 29 2009

Status

approved