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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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 * A256175 A236861 A016300

Adjacent sequences:  A322671 A322672 A322673 * A322675 A322676 A322677

KEYWORD

nonn,easy,base,tabl

AUTHOR

Jan Koornstra, Jan 22 2019

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)