A061859 -id:A061859 - cp's OEIS frontend

A061858 Differences between the ordinary multiplication table A004247 and the carryless multiplication table for GF(2)[X] polynomials A048720, i.e., the effect of the carry bits in binary multiplication.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 12, 0, 8, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 24, 0, 0, 0

Offset: 0

Antti Karttunen, May 11 2001

			From _Peter Munn_, Jan 28 2021: (Start)
The top left 12 X 12 corner of the table:
      |  0   1   2   3   4   5   6   7   8   9  10  11
------+------------------------------------------------
   0  |  0   0   0   0   0   0   0   0   0   0   0   0
   1  |  0   0   0   0   0   0   0   0   0   0   0   0
   2  |  0   0   0   0   0   0   0   0   0   0   0   0
   3  |  0   0   0   4   0   0   8  12   0   0   0   4
   4  |  0   0   0   0   0   0   0   0   0   0   0   0
   5  |  0   0   0   0   0   8   0   8   0   0  16  16
   6  |  0   0   0   8   0   0  16  24   0   0   0   8
   7  |  0   0   0  12   0   8  24  28   0   0  16  28
   8  |  0   0   0   0   0   0   0   0   0   0   0   0
   9  |  0   0   0   0   0   0   0   0   0  16   0  16
  10  |  0   0   0   0   0  16   0  16   0   0  32  32
  11  |  0   0   0   4   0  16   8  28   0  16  32  52
(End)

"Zoomed in" variant: A061859.
Rows/columns 3, 5 and 7 are given by A048728, A048729, A048730.
Main diagonal divided by 4: A213673.
Numbers that generate no carries when multiplied in binary by 11_2: A003714, by 101_2: A048716, by 1001_2: A115845, by 10001_2: A115847, by 100001_2: A114086.
Other sequences related to the presence/absence of a carry in binary multiplication: A116361, A235034, A235040, A236378, A266195, A289726.

a(n) = A004247(n) - A048720(n).

cp's OEIS Frontend

A061858 Differences between the ordinary multiplication table A004247 and the carryless multiplication table for GF(2)[X] polynomials A048720, i.e., the effect of the carry bits in binary multiplication.

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