A265008 -id:A265008 - cp's OEIS frontend

A265183 Base-10 analog of Marko Riedel's A265008, but allowing A, B, C to be zero.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 1, 1, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 1, 0, 0, 1, 5, 5, 1, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0

Offset: 0

N. J. A. Sloane, Dec 04 2015

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A265008, A265182, A265236.

Cf. A218978.

a265183 n = length [() | let cs = a218978_row n, a <- cs, b <- cs, c <- cs,
                         a * b == c || c == 0 && a * b == 0]
-- Reinhard Zumkeller, Dec 05 2015

Data corrected by Reinhard Zumkeller, Dec 05 2015

A265182 Base-10 analog of Marko Riedel's A265008.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 0, 1, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 1, 0, 0, 1, 0, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0

Offset: 1

N. J. A. Sloane, Dec 04 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A265008, A265236.
See A265183 for the version where A, B, C may be zero.
Cf. A218978.

a265182 n = length [() | let cs = dropWhile (== 0) $ a218978_row n, c <- cs,
            let as = takeWhile (<= c) cs, a <- as, b <- as, a * b == c]
-- Reinhard Zumkeller, Dec 05 2015

F:= proc(n) local L, ss;
  L:= convert(n, base, 10);
  ss:= {seq(seq(add(10^(i-j)*L[i], i=j..k), j=1..k), k=1..nops(L))} minus {0};
  numboccur(true, [seq(seq(member(a*b, ss), a=ss), b=ss)]);
end proc:
seq(F(n), n=1..1000); # Robert Israel, Dec 06 2015

Corrected by Lars Blomberg, Dec 05 2015

A265236 Number of solutions to the equation A x B = C, where A, B and C are nonnegative numbers appearing as (contiguous) substrings of the binary representation of n.

Original entry on oeis.org

1, 1, 8, 3, 13, 12, 18, 5, 19, 17, 18, 20, 31, 26, 28, 7, 26, 23, 23, 26, 31, 22, 32, 28, 47, 40, 38, 34, 49, 40, 38, 9, 34, 30, 29, 31, 31, 31, 38, 34, 47, 39, 28, 34, 53, 40, 46, 38, 66, 55, 54, 48, 59, 46, 46, 48, 75, 62, 58, 52, 67, 58, 48, 11, 43, 38

Offset: 0

Reinhard Zumkeller, Dec 06 2015

nonn

A, B and C are allowed to be zero, in contrast to A265008;
a(A000225(n)) = A265008(A000225(n));
a(A062289(n)) != A265008(A062289(n)).

			.  n | A007088 | A119709     |  a |
. ---+---------+-------------+----+-------------------------------------
.  2 |      10 | [0,1,2]     |  8 = #{(0,0,0), (0,1,0), (0,2,0), (1,0,0),
.    |         |             |        (2,0,0), (1,1,1), (1,2,2), (2,1,2)}
.  3 |      11 | [1,3]       |  3 = #{(1,1,1), (1,3,3), (3,1,3)}
.  4 |     100 | [0,1,2,4]   | 13 = #{(0,0,0), (0,1,0), (0,2,0), (0,4,0),
.    |         |             |         (1,0,0), (2,0,0), (4,0,0), (1,1,1),
.    |         |             |         (1,2,2), (2,1,2), (1,4,4), (2,2,4),
.    |         |             |         (4,1,4)}
.  5 |     101 | [0,1,2,5]   | 12 = #{(0,0,0), (0,1,0), (0,2,0), (0,5,0),
.    |         |             |         (1,0,0), (2,0,0), (5,0,0), (1,1,1),
.    |         |             |         (1,2,2), (2,1,2), (1,5,5), (5,1,5)}
.  6 |     110 | [0,1,2,3,6] | 18 = #{(0,0,0), (0,1,0), (0,2,0), (0,3,0),
.    |         |             |         (0,6,0), (1,0,0), (2,0,0), (3,0,0),
.    |         |             |         (6,0,0), (1,1,1), (1,2,2), (2,1,2),
.    |         |             |         (1,3,3), (3,1,3), (1,6,6), (2,3,6),
.    |         |             |         (3,2,6), (6,1,6)}
.  7 |     111 | [1,3,7]     |≈ 5 = #{(1,1,1), (1,3,3), (3,1,3), (1,7,7),
.    |         |             |         (7,1,7)} .

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A007088, A119709, A265008, A265183 (decimal case), A000225, A062289, A043545, A078822.

a265236 n = length [() | let cs = a119709_row n, a <- cs, b <- cs, c <- cs,
                         a * b == c || c == 0 && a * b == 0]

For n > 0: a(n) = A265008(n) + A043545(n) * (2*A078822(n) - 1).

Suggested by N. J. A. Sloane.

cp's OEIS Frontend

A265183 Base-10 analog of Marko Riedel's A265008, but allowing A, B, C to be zero.

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A265182 Base-10 analog of Marko Riedel's A265008.

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A265236 Number of solutions to the equation A x B = C, where A, B and C are nonnegative numbers appearing as (contiguous) substrings of the binary representation of n.

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