A322674 Square array read by antidiagonals: T(n, k) = 1 if the digits of p = n*k in base 2 are exactly the same as the digits of p when considering the base-2 representations of n, k and p as base-10 numbers, otherwise T(n, k) = 0.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0

Comments

As n * k = k * n, the array is symmetric.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array

Jan Koornstra, Graph of all pairs up to (1024, 1024)

Index entries for characteristic functions

Example

In base 2, 1001 * 10100 = 10110100. In base 10, 1001 * 10100 = 10110100. These digits match and therefore the pairs T(9, 20) and T(20, 9) are a 1 in the sequence (at a(444) and a(455)).
In base 2, the product of 11 * 11 = 1001, whereas 11 * 11 in base 10 yields 121. T(3, 3) is the 24th pair in the sequence and the first to fail. a(24) is thus a 0.
The array begins:
  1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 1, 1, 0, 1, 1, 0, 0, 1, ...
  1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 1, 1, 1, 1, 0, 1, 0, 1, ...
  1, 1, 1, 0, 1, 1, 0, 0, 1, ...
  1, 1, 1, 0, 1, 0, 0, 0, 1, ...
  1, 1, 1, 1, 1, 1, 1, 1, 1, ...

Prog

(Python 3)
def a322674(k):
  seq = []
  i = 0
  while len(seq) <= k:
    j = 0
    while len(seq) <= k and j < i + 1:
      n = i - j
      m = j
      decn = int(bin(n).replace('0b', ''))
      decm = int(bin(m).replace('0b', ''))
      binProd = bin(n * m).replace('0b', '')
      decProd = str(decn * decm)
      seq.append(int(binProd == decProd))
      j += 1
    i += 1
  print(seq)
a322674(100)
(PARI) T(n, k) = fromdigits(binary(n))*fromdigits(binary(k)) == fromdigits(binary(n*k)); \\ Michel Marcus, Apr 03 2019

Crossrefs

Cf. A071998, A007088, A257831, A080719.

Sequence in context: A014676 A015343 A296077 * A236861 A016300 A016126

Adjacent sequences: A322671 A322672 A322673 * A322675 A322676 A322677

Keyword

nonn,easy,base,tabl

Author

Jan Koornstra, Jan 22 2019

Status

approved