A391245 Triangular table T(n,k) = n*k if A048720(n, A065621(k)) = n*k, otherwise 0, read by rows for n >= 1, 1 <= k <= n.

1, 2, 4, 3, 6, 9, 4, 8, 0, 16, 5, 10, 0, 20, 0, 6, 12, 18, 24, 0, 36, 7, 14, 21, 28, 35, 42, 49, 8, 16, 0, 32, 0, 0, 0, 64, 9, 18, 0, 36, 0, 0, 0, 72, 0, 10, 20, 0, 40, 0, 0, 0, 80, 0, 0, 11, 22, 0, 44, 0, 0, 0, 88, 0, 0, 0, 12, 24, 36, 48, 0, 72, 0, 96, 0, 0, 132, 144, 13, 26, 0, 52, 0, 0, 0, 104, 0, 0, 0, 0, 0

Offset

1,2

Comments

T(n,k) = 0 unless n*k can be computed correctly with a shortcut binary carryless multiplication formula as n*k = A048720(n, A065621(k)), in which case T(n,k) = A075362(n, k) = n*k.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 rows of triangle

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to carryless arithmetic.

Example

Triangle begins as:
   1;
   2,  4;
   3,  6,  9;
   4,  8,  0, 16;
   5, 10,  0, 20,  0;
   6, 12, 18, 24,  0, 36;
   7, 14, 21, 28, 35, 42, 49;
   8, 16,  0, 32,  0,  0,  0,  64;
   9, 18,  0, 36,  0,  0,  0,  72,  0;
  10, 20,  0, 40,  0,  0,  0,  80,  0,  0;
  11, 22,  0, 44,  0,  0,  0,  88,  0,  0,   0;
  12, 24, 36, 48,  0, 72,  0,  96,  0,  0, 132, 144;
  13, 26,  0, 52,  0,  0,  0, 104,  0,  0,   0,   0,  0;
  etc.

Prog

(PARI)
up_to = 91;
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A391245_tr(x, y) = if(x*y == A048720(x, A065621(y)), x*y, 0);
A391245list(up_to) = { my(v = vector(up_to), i=0); for(n=1, oo, for(k=1, n, if(i++ > up_to, return(v)); v[i] = A391245_tr(n, k))); (v); };
v391245 = A391245list(up_to);
A391245(n) = v391245[n];

Crossrefs

Cf. A048720, A065621, A277199.

Cf. triangular tables A075362 and A391244.

Cf. A391246 (how many times each n occurs in this table), A391247 (numbers that occur only once).

Cf. A023758 (seems to give the indices of the nonzero terms on the right edge. See also A277704, A277807)

Sequence in context: A077661 A077583 A153125 * A359697 A139413 A075362

Adjacent sequences: A391242 A391243 A391244 * A391246 A391247 A391248

Keyword

nonn,tabl

Author

Antti Karttunen, Dec 06 2025

Status

approved