A048962 -id:A048962 - cp's OEIS frontend

A048963 Table in which n-th row lists digits in periodic part of decimal expansion of reciprocal of n-th prime.

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

Offset: 1

N. J. A. Sloane

The length of row n is A048595(n). - T. D. Noe, May 14 2008
The convention is that the earliest period is displayed. - T. D. Noe, May 14 2008
Conjecture: regarded as a decimal fraction, this number is normal in base 10. - Franklin T. Adams-Watters, Aug 20 2012

			1/2=.5 ->0; 1/3=.3333... -> 3; 1/5=.2 ->0; 1/7=.142857... -> 1 4 2 8 5 7; etc.
0; 3; 0; 1,4,2,8,5,7; 0,9; 7,6,9,2,3,0; 5,8,8,2,3,5,2,9,4,1,1,7,6,4,7,0; ...

Conway and Guy, The Book of Numbers, p. 160

Cf. A048962.

Clear[d]; d[{{2|5}, 0}] = {0}; d[{{{n__}}, 0}] := {n}; d[{{{n__, 0}}, k_?Negative}] := Join[Table[0, {-k}], Drop[{n}, k+1]]; A048963 = d /@ RealDigits[1/Prime[Range[10]]] (* Jean-François Alcover, Dec 10 2014 *)

A048997 Sum of digits in decimal expansion of 1/n up to the point where it repeats for the first time.

Original entry on oeis.org

1, 5, 3, 7, 2, 7, 27, 8, 1, 1, 9, 11, 27, 27, 6, 13, 72, 5, 81, 5, 27, 9, 99, 11, 4, 27, 10, 30, 126, 3, 54, 11, 3, 72, 27, 9, 9, 81, 18, 7, 18, 27, 90, 11, 2, 99, 207, 13, 189, 2, 69, 28, 63, 14, 9, 35, 81, 126, 261, 7, 270, 54, 24, 19, 27, 6, 144, 73, 96, 27, 126, 12, 36, 9, 4

Offset: 1

Deepak R. N (deepak_rama(AT)bigfoot.com)

			1/1=1. -> 1; 1/2=.5 ->5; 1/3=.3333... -> 3; 1/4=.25 -> 7; 1/5=.2 ->2; 1/6=.1666... -> 7; 1/7=.142857... -> 27; etc.

Index entries for sequences related to decimal expansion of 1/n

Cf. A048962.

Table[Total[Flatten[RealDigits[1/n][[1]]]], {n, 1, 75}] (* Jean-François Alcover, Mar 15 2011 *)

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 17 2001

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.

Original entry on oeis.org

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

Chittaranjan Pardeshi, Jun 17 2022

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

			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, ...

Cf. A020806, A021017, A021018.
Cf. A048962, A257927.
Cf. A061480 (diagonal).
Cf. A355202 (binary).

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

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

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

A079483 Array read by rows in which n-th row lists the periodic part of the base-n expansion of 1/7.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 3, 2, 4, 1, 2, 0, 5, 0, 1, 1, 2, 5, 1, 4, 2, 8, 5, 7, 1, 6, 3, 1, 8, 6, 10, 3, 5, 1, 11, 0, 2, 2, 4, 9, 2, 7, 4, 14, 9, 12, 2, 10, 5, 2, 13, 10, 16, 5, 8, 2, 17, 0, 3, 3, 6, 13, 3, 10, 6, 20, 13, 17, 3, 14, 7, 3, 18, 14

Offset: 2

Stephen K. Johnson, Jan 17 2003

			In base 2, 1/111_2 = 0.001001001001 ..., where 111_2 = 7; the periodic part is 0 0 1, so these form the first three digits. The periodic portions in the next few bases are 010212 (base 3), 021 (base 4), etc.
Array begins:
  0, 0, 1;
  0, 1, 0, 2, 1, 2;
  0, 2, 1;
  0, 3, 2, 4, 1, 2;
  0, 5;
  ...

Cf. A048962, A048963, A020806, A035613.

More terms from Sean A. Irvine, Aug 16 2025

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A048963 Table in which n-th row lists digits in periodic part of decimal expansion of reciprocal of n-th prime.

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A048997 Sum of digits in decimal expansion of 1/n up to the point where it repeats for the first time.

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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.

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A079483 Array read by rows in which n-th row lists the periodic part of the base-n expansion of 1/7.

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