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

1,2

Comments

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

Links

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

Formula

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

Example

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, ...

Prog

(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

Crossrefs

Cf. A020806, A021017, A021018.

Cf. A048962, A257927.

Cf. A061480 (diagonal).

Cf. A355202 (binary).

Sequence in context: A051566 A051567 A361980 * A261219 A085850 A176867

Adjacent sequences: A355065 A355066 A355067 * A355069 A355070 A355071

Keyword

base,easy,nonn,tabl

Author

Chittaranjan Pardeshi, Jun 17 2022

Status

approved