A048997 -id:A048997 - 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 *)

A244661 Beastly reciprocals, or numbers n such that digitsum(1/n) = 666.

Original entry on oeis.org

149, 298, 596, 646, 745, 1192, 1490, 1615, 2119, 2584, 2980, 3109, 3725, 3878, 5960, 6218, 6357, 6460, 7106, 7294, 7450, 8476, 9262, 9868, 10941, 11627, 11634, 11920, 12436, 14535, 14900, 15049, 15545, 16150, 18625, 21190, 22718, 23256, 23902, 24872, 24915

Offset: 1

Anthony Sand, Jul 04 2014

149 is a full reptend prime (see A001913), hence the sum of the decimal digits of 1/149 is 9 * 148 / 2 = 666.
From Robert G. Wilson v, Aug 16 2014: (Start)
If n is present, so is 10n.
If n is present then A003592*n is possibly present.
Primitives are: 149, 646, 1615, 2119, 3109, 3878, 7294, 9262, 9868, 10941, …, .
Palindromes: 646, 1525251, 2062602, …, .
Primes: 149, 3109, 111149, 351391, …, .
(End)

			If digitsum(1/n) sums the decimal digits of 1/n up to the point at which they recur or terminate, then digitsum(1/149) = 666 = 0 + 0 + 6 + 7 + 1 + 1 + 4 + 0 + 9 + 3 + 9 + 5 + 9 + 7 + 3 + 1 + 5 + 4 + 3 + 6 + 2 + 4 + 1 + 6 + 1 + 0 + 7 + 3 + 8 + 2 + 5 + 5 + 0 + 3 + 3 + 5 + 5 + 7 + 0 + 4 + 6 + 9 + 7 + 9 + 8 + 6 + 5 + 7 + 7 + 1 + 8 + 1 + 2 + 0 + 8 + 0 + 5 + 3 + 6 + 9 + 1 + 2 + 7 + 5 + 1 + 6 + 7 + 7 + 8 + 5 + 2 + 3 + 4 + 8 + 9 + 9 + 3 + 2 + 8 + 8 + 5 + 9 + 0 + 6 + 0 + 4 + 0 + 2 + 6 + 8 + 4 + 5 + 6 + 3 + 7 + 5 + 8 + 3 + 8 + 9 + 2 + 6 + 1 + 7 + 4 + 4 + 9 + 6 + 6 + 4 + 4 + 2 + 9 + 5 + 3 + 0 + 2 + 0 + 1 + 3 + 4 + 2 + 2 + 8 + 1 + 8 + 7 + 9 + 1 + 9 + 4 + 6 + 3 + 0 + 8 + 7 + 2 + 4 + 8 + 3 + 2 + 2 + 1 + 4 + 7 + 6 + 5 + 1.

Robert G. Wilson v, Table of n, a(n) for n = 1..546

Cf. A048997, A238104, A051003, A001913.

fQ[n_] := Total[ RealDigits[ 1/n, 10][[1, 1]]] == 666;  Select[ Range@ 25000, fQ ] (* Robert G. Wilson v, Aug 16 2014 *)

A244592 Numbers n such that n equals the partial or complete sum of the decimal digits of 1/n, up to the point at which the digits recur or terminate.

Original entry on oeis.org

3, 7, 8, 13, 14, 34, 43, 49, 51, 76, 83, 92, 94, 98, 103, 109, 113, 127, 139, 141, 169, 177, 179, 181, 194, 218, 229, 283, 323, 338, 367, 394, 397, 401, 437, 524, 526, 537, 579, 587, 626, 659, 661, 673, 674, 687, 701, 719, 724, 743, 767, 769, 802, 823, 838

Offset: 1

Anthony Sand, Jul 01 2014

The digits summed are those before the decimal expansion recurs or terminates. Otherwise reciprocals that supply a recurrent 1, like 1/9 = 0.111... or 1/99 = 0.010101..., would always produce a sum equal to n from sufficient terms of the reciprocal.

			1/3 = 0.3... and 3 = 0 + 3.
1/7 = 0.142857... and 7 = 1 + 4 + 2.
1/8 = 0.125 and 8 = 1 + 2 + 5.
1/13 = 0.0769230... and 13 = 7 + 6.
1/14 = 0.0714285... and 14 = 7 + 1 + 4 + 2.
1/34 = 0.02941176470588235... and 34 = 2 + 9 + 4 + 1 + 1 + 7 + 6 + 4.

Cf. A048997.

cp's OEIS Frontend

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

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A244661 Beastly reciprocals, or numbers n such that digitsum(1/n) = 666.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A244592 Numbers n such that n equals the partial or complete sum of the decimal digits of 1/n, up to the point at which the digits recur or terminate.

Views

Author

Keywords

Comments

Examples

Crossrefs