A271710 Table T(n,k) = 2^n XOR 2^k read by antidiagonals, where XOR is the binary exclusive or operator.

0, 3, 3, 5, 0, 5, 9, 6, 6, 9, 17, 10, 0, 10, 17, 33, 18, 12, 12, 18, 33, 65, 34, 20, 0, 20, 34, 65, 129, 66, 36, 24, 24, 36, 66, 129, 257, 130, 68, 40, 0, 40, 68, 130, 257, 513, 258, 132, 72, 48, 48, 72, 132, 258, 513, 1025, 514, 260, 136, 80, 0, 80, 136, 260

Offset

0,2

Comments

n > 1 is in this sequence if and only if it is in A018900.

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Formula

T(n, k) = 0 if n = k.

T(n, k) = A271709(n, k) if n != k.

Example

a(0) = T(0, 0) = 2^0 XOR 2^0 = 0.
a(1) = T(1, 0) = 2^1 XOR 2^0 = 3.
   0,   3,   5,   9,  17,  33,  65, 129, 257, 513,1025,
   3,   0,   6,  10,  18,  34,  66, 130, 258, 514,1026,
   5,   6,   0,  12,  20,  36,  68, 132, 260, 516,1028,
   9,  10,  12,   0,  24,  40,  72, 136, 264, 520,1032,
  17,  18,  20,  24,   0,  48,  80, 144, 272, 528,1040,
  33,  34,  36,  40,  48,   0,  96, 160, 288, 544,1056,
  65,  66,  68,  72,  80,  96,   0, 192, 320, 576,1088,
 129, 130, 132, 136, 144, 160, 192,   0, 384, 640,1152,
 257, 258, 260, 264, 272, 288, 320, 384,   0, 768,1280,
 513, 514, 516, 520, 528, 544, 576, 640, 768,   0,1536,
1025,1026,1028,1032,1040,1056,1088,1152,1280,1536,   0,

Maple

read("transforms") ;
A271710 := proc(n, k)
    XORnos(2^n, 2^k) ;
end proc: # R. J. Mathar, Apr 15 2016

Mathematica

Table[BitXor[2^(n - k), 2^k], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Apr 12 2016 *)

Prog

(PARI) T(n, k) = bitxor(2^n, 2^k);
matrix(10, 10, n, k, n--; k--; T(n, k)) \\ Michel Marcus, Apr 12 2016

Crossrefs

Cf. A271709.

Sequence in context: A011445 A197137 A133456 * A371659 A246005 A103786

Adjacent sequences: A271707 A271708 A271709 * A271711 A271712 A271713

Keyword

nonn,tabl,easy

Author

Peter Kagey, Apr 12 2016

Status

approved