A355202 - OEIS

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

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OFFSET

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