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