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A054238 T(i,j) = bits of binary expansion of i interleaved with that of j. 26
0, 1, 2, 4, 3, 8, 5, 6, 9, 10, 16, 7, 12, 11, 32, 17, 18, 13, 14, 33, 34, 20, 19, 24, 15, 36, 35, 40, 21, 22, 25, 26, 37, 38, 41, 42, 64, 23, 28, 27, 48, 39, 44, 43, 128, 65, 66, 29, 30, 49, 50, 45, 46, 129, 130, 68, 67, 72, 31, 52, 51, 56, 47, 132, 131, 136, 69, 70, 73, 74 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Inverse of sequence A054239 considered as a permutation of the nonnegative integers.

Permutation of nonnegative integers. Can be used as natural alternate number casting for pairs/tables (vs. usual diagonalization).

Table T(n,k), read by antidiagonals, defined by T(n,k) = A000695(k) + 2*A000695(n). - Philippe Deléham, Oct 18 2011

This array is a Z-order curve in an N x N grid. - Max Barrentine, Sep 24 2015

Each row n of this array is the lexicographically earliest sequence such that no term occurs in a previous row, no three terms form an arithmetic progression, and the k-th term in the n-th row is equal to the k-th term in row 0 plus some constant (specifically, T(n,k)=T(0,k)+A062880(n)). - Max Barrentine, Jul 20 2016

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Wikipedia, Z-order Curve

Index entries for sequences that are permutations of the natural numbers

FORMULA

From Robert Israel, Jul 21 2016: (Start)

G.f. of array: g(x,y) = (1/(1-x)*(1-y)) * Sum_{i>=0}

(2^(2*i+1)*x^(2^i)/(1+x^(2^i)) + 2^(2*i)*y^(2^i)/(1+y^(2^i))).

T(2*n+i,2*k+j) = 4*T(n,k) + 2*i+j for i,j in {0,1}. (End)

EXAMPLE

T(5,6)=57 because .1.0.1 (5) merged with 1.1.0. (6) is 111001 (57).

The array starts in row n=0 with columns k>=0 as follows:

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

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

8...9..12..13..24..25..28..29...

10.11..14..15..26..27..30..31...

32.33..36..37..48..49..52..53...

34.35..38..39..50..51..54..55...

40.41..44..45..56..57..60..61...

42.43..46..47..58..59..62..63...

- Philippe Deléham, Oct 18 2011

MAPLE

N:= 4: # to get the first 2^(2N+1)+2^N terms

G:= 1/(1-y)/(1-x)*(add(2^(2*i+1)*x^(2^i)/(1+x^(2^i)), i=0..N) + add(2^(2*i)*y^(2^i)/(1+y^(2^i)), i=0..N)):

S:= mtaylor(G, [x=0, y=0], 2^(N+1)):

seq(seq(coeff(coeff(S, x, i), y, m-i), i=0..m), m=0..2^(N+1)-1); # Robert Israel, Jul 21 2016

MATHEMATICA

Table[Total@ Map[FromDigits[#, 2] &, Insert[#, 0, {-1, -1}] &@ Map[Riffle[IntegerDigits[#, 2], 0, 2] &, {n - k, k}]], {n, 0, 11}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jul 21 2016 *)

CROSSREFS

Cf. A000695, A062880.

See also A163357 and A163334 for other fractal curves in N x N grids.

Sequence in context: A269375 A135141 A098709 * A225589 A245603 A048679

Adjacent sequences:  A054235 A054236 A054237 * A054239 A054240 A054241

KEYWORD

easy,nonn,base,tabl

AUTHOR

Marc LeBrun, Feb 07 2000

STATUS

approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)