A268834 Transpose of array A268833.

0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 2, 3, 2, 1, 0, 3, 2, 3, 2, 1, 0, 2, 1, 2, 1, 2, 1, 0, 1, 2, 3, 2, 3, 2, 1, 0, 2, 3, 4, 3, 2, 1, 2, 1, 0, 3, 2, 3, 4, 3, 2, 1, 2, 1, 0, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 0, 3, 4, 1, 2, 3, 4, 3, 2, 3, 2, 1, 0, 2, 3, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1, 0, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 0, 2, 1, 2, 1, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 0

Offset

0,4

Comments

See comments in A268833.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8255; the first 128 antidiagonals of array

Example

The top left [0 .. 16] x [0 .. 16] section of the array:
  0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2
  0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2
  0, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2
  0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 4, 3, 2
  0, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2
  0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2
  0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 2
  0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2
  0, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2
  0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2
  0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 2
  0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2
  0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2
  0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2
  0, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2
  0, 1, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 4, 3, 2
  0, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 3, 2

Mathematica

A101080[n_, k_]:= DigitCount[BitXor[n, k], 2, 1]; A003188[n_]:=BitXor[n, Floor[n/2]]; A006068[n_]:=If[n<2, n, Block[{m=A006068[Floor[n/2]]}, 2m + Mod[Mod[n, 2] + Mod[m, 2], 2]]]; a[r_, 0]:= 0; a[0, c_]:=c; a[r_, c_]:= A003188[1 + A006068[a[r - 1, c - 1]]]; A[r_, c_]:=A101080[c, a[r, r + c]]; Table[A[r - c, c], {r, 0, 20}, {c, 0, r}] // Flatten (* Indranil Ghosh, Apr 02 2017 *)

Prog

(Scheme)
(define (A268834 n) (A268833bi (A025581 n) (A002262 n))) ;; Code for A268833bi given in A268833.
(PARI) b(n) = if(n<1, 0, b(n\2) + n%2);
A101080(n, k) = b(bitxor(n, k));
A003188(n) = bitxor(n, n\2);
A006068(n) = if(n<2, n, {my(m = A006068(n\2)); 2*m + (n%2 + m%2)%2});
A268820(r, c) = if(r==0, c, if(c==0, 0, A003188(1 + A006068(A268820(r - 1, c - 1)))));
A(r, c) = A101080(c, A268820(r, r + c));
for(r=0, 20, for(c=0, r, print1(A(r - c, c), ", "); ); print(); ) \\ Indranil Ghosh, Apr 02 2017
(Python)
def A101080(n, k): return bin(n^k)[2:].count("1")
def A003188(n): return n^(n/2)
def A006068(n):
....if n<2: return n
....else:
........m=A006068(n/2)
........return 2*m + (n%2 + m%2)%2
def A268820(r, c): return c if r<1 else 0 if c<1 else A003188(1 + A006068(A268820(r - 1, c - 1)))
def a(r, c): return A101080(c, A268820(r, r + c))
for r in range(0, 21):
....print [a(r - c, c) for c in range(0, r + 1)] # Indranil Ghosh, Apr 02 2017

Crossrefs

Transpose of A268833.

Sequence in context: A025870 A104276 A216191 * A285914 A096875 A194514

Adjacent sequences: A268831 A268832 A268833 * A268835 A268836 A268837

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 15 2016

Status

approved