A355202 Square array read by upwards antidiagonals: T(n,k) = k-th binary digit after the radix point of 1/n, for n >= 1 and k >= 1.

0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0

Offset

1

Comments

First row is all zeros since n=1 has all zeros after the radix point in binary base 2.

Period of n-th row = A007733(n).

Links

Table of n, a(n) for n=1..87.

Formula

T(n,k) = 1 iff 2 * (2^(k-1) mod n) >= n.

Example

Array begins:
      k=1  2  3  4  5  6  7  8
  n=1:  0, 0, 0, 0, 0, 0, 0, 0,
  n=2:  1, 0, 0, 0, 0, 0, 0, 0,
  n=3:  0, 1, 0, 1, 0, 1, 0, 1,
  n=4:  0, 1, 0, 0, 0, 0, 0, 0,
  n=5:  0, 0, 1, 1, 0, 0, 1, 1,
  n=6:  0, 0, 1, 0, 1, 0, 1, 0,
  n=7:  0, 0, 1, 0, 0, 1, 0, 0,
  n=8:  0, 0, 1, 0, 0, 0, 0, 0,
Row n=7 is 1/7 = .001001001001..., whose digits after the radix point are 0,0,1,0,0,1,0,0, ...

Prog

(PARI) T(n, k) = my(r=lift(Mod(2, n)^(k-1))); 2*r>=n;
(Python) def T(n, k): return (2*pow(2, k-1, n)//n)

Crossrefs

Cf. A007733, A355068 (decimal digits).

Sequence in context: A162518 A330306 A300477 * A353556 A228495 A356982

Adjacent sequences: A355199 A355200 A355201 * A355203 A355204 A355205

Keyword

base,easy,nonn,tabl

Author

Chittaranjan Pardeshi, Jun 23 2022

Status

approved