A048963 -id:A048963 - cp's OEIS frontend

A048962 Table in which n-th row lists digits in periodic part of decimal expansion of 1/n.

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

Offset: 1

N. J. A. Sloane

The length of row n is A007732(n). - T. D. Noe, May 14 2008

The convention is that the earliest period is displayed. - T. D. Noe, May 14 2008

			1/1=1. -> 0; 1/2=.5 ->0; 1/3=.3333... -> 3; 1/4=.25 -> 0; 1/5=.2 ->0; 1/6=.1666... -> 6; 1/7=.142857... -> 1 4 2 8 5 7; etc.
Triangle begins:
  0;
  0;
  3;
  0;
  0;
  6;
  1,4,2,8,5,7;
  0;
  1;
  0;
  0,9;
  3;
  0,7,6,9,2,3;
  7,1,4,2,8,5;
  6;
  0;
  ...

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

Cf. A048997, A048963.

nmax = 50;
row[n_] := Switch[FactorInteger[n], {{2, }} | {{5, }} | {{2, }, {5, }}, {0}, _, rd = RealDigits[N[1 + 1/n, 10 nmax]]; FindTransientRepeat[rd[[1]] // Rest, 2][[2]]];
row /@ Range[nmax] // Flatten (* Jean-François Alcover, Dec 04 2019 *)

A236184 Decimal expansion of 1/65537.

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Jan 19 2014

Periodic sequence of period 65536. Being a Fermat prime > 5, 65537 is a full reptend prime. One full period is given in the table.

			0.000015258556235409005599890138395105055159680791003555243602850298304774...

Rick L. Shepherd, Table of n, a(n) for n = 0..65535
MathWorld, Fermat Prime

Cf. A007450 (1/17), A021261 (1/257), A019434, A001913, A048963.

RealDigits[1/65537, 10, 105, -1][[1]] (* T. D. Noe, Jan 27 2014 *)

{default(realprecision, 66000);
x = 1/65537; d = 0; for(n = 0, 65535, x = (x-d)*10; d = floor(x);
write("b236184.txt", n, " ", d))} \\ Rick L. Shepherd, Jan 19 2014 (after similar program by Harry J. Smith)

a(n + 65536) = a(n).

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

cp's OEIS Frontend

A048962 Table in which n-th row lists digits in periodic part of decimal expansion of 1/n.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

A236184 Decimal expansion of 1/65537.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Examples

Crossrefs

Extensions