A355068 Square array read by upwards antidiagonals: T(n,k) = k-th digit after the decimal point in decimal expansion of 1/n, for n >= 1 and k >= 1.

0, 5, 0, 3, 0, 0, 2, 3, 0, 0, 2, 5, 3, 0, 0, 1, 0, 0, 3, 0, 0, 1, 6, 0, 0, 3, 0, 0, 1, 4, 6, 0, 0, 3, 0, 0, 1, 2, 2, 6, 0, 0, 3, 0, 0, 1, 1, 5, 8, 6, 0, 0, 3, 0, 0, 0, 0, 1, 0, 5, 6, 0, 0, 3, 0, 0, 0, 9, 0, 1, 0, 7, 6, 0, 0, 3, 0, 0, 0, 8, 0, 0, 1, 0, 1, 6, 0

Offset: 1

Author

Chittaranjan Pardeshi, Jun 17 2022

Keywords

• base
• easy
• nonn
• tabl

Comments

First row is all zeros since n=1 has all zeros after the decimal point.

Examples

			Array begins:
      k=1  2  3  4  5  6  7  8
  n=1:  0, 0, 0, 0, 0, 0, 0, 0,
  n=2:  5, 0, 0, 0, 0, 0, 0, 0,
  n=3:  3, 3, 3, 3, 3, 3, 3, 3,
  n=4:  2, 5, 0, 0, 0, 0, 0, 0,
  n=5:  2, 0, 0, 0, 0, 0, 0, 0,
  n=6:  1, 6, 6, 6, 6, 6, 6, 6,
  n=7:  1, 4, 2, 8, 5, 7, 1, 4,
  n=8:  1, 2, 5, 0, 0, 0, 0, 0,
Row n=7 is 1/7 = .142857142857..., whose digits after the decimal point are 1,4,2,8,5,7,1,4,2,8,5,7, ...
		

Crossrefs

Cf. A020806, A021017, A021018.

Cf. A048962, A257927.

Cf. A061480 (diagonal).

Cf. A355202 (binary).

Programs

PARI

T(n,k) = my(r=lift(Mod(10,n)^(k-1))); floor(10*r/n)%10;

Python

def T(n,k): return (10*pow(10,k-1,n)//n)%10

Formula

1/n = Sum_{k>=1} T(n, k)*10^-k, for n > 1.