A369312 - OEIS

A369312

Square array A(n, k), n >= 0, k > 0, read by upwards antidiagonals: P(A(n, k)) is the quotient of the polynomial long division of P(n) by P(k) (where P(m) denotes the polynomial over GF(2) whose coefficients are encoded in the binary expansion of the nonnegative integer m).

0, 1, 0, 2, 0, 0, 3, 1, 0, 0, 4, 1, 1, 0, 0, 5, 2, 1, 0, 0, 0, 6, 2, 3, 0, 0, 0, 0, 7, 3, 3, 1, 0, 0, 0, 0, 8, 3, 2, 1, 1, 0, 0, 0, 0, 9, 4, 2, 1, 1, 1, 0, 0, 0, 0, 10, 4, 7, 1, 1, 1, 1, 0, 0, 0, 0, 11, 5, 7, 2, 1, 1, 1, 0, 0, 0, 0, 0, 12, 5, 6, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

For any number m >= 0 with binary expansion Sum_{k >= 0} b_k * 2^k, P(m) = Sum_{k >= 0} b_k * X^k.

LINKS

Table of n, a(n) for n=0..90.

Index entries for sequences operating on GF(2)[X]-polynomials

EXAMPLE

Array A(n, k) begins:

n\k | 1 2 3 4 5 6 7 8 9 10 11 12

----+---------------------------------------