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

Author

Antti Karttunen, Jul 29 2009

Keywords

• nonn
• tabl

Comments

The top left 8x8 corner of this array

+0 +2 10 [phone]

+1 +3 11 [phone]

+5 [phone]

+4 [phone]

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

• Antti Karttunen, Table of n, a(n) for n = 0..2079
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

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 *)

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

Scheme

(define (A163235 n) (A163233bi (A002262 n) (A025581 n)))