A020806 -id:A020806 - cp's OEIS frontend

A021018 Decimal expansion of 1/14.

0, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1

Offset: 0

N. J. A. Sloane

			0.0714285714285...

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Cf. A020806.

First[RealDigits[1/14, 10, 100, -1]] (* Paolo Xausa, Sep 16 2024 *)

A153110 Period 6: repeat [1, 5, 7, 2, 4, 8].

Original entry on oeis.org

1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8, 1, 5, 7, 2, 4, 8

Offset: 0

Paul Curtz, Dec 18 2008

Also A141425^5 mod 9. See A020806.

Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1).

Cf. A020806, A038194, A141425.

&cat[[1, 5, 7, 2, 4, 8]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

A153110:=n->(9-cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6))/2: seq(A153110(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016

PadLeft[{},90,{1,5,7,2,4,8}] (* Harvey P. Dale, Sep 10 2011 *)

a(n)=[1,2,4,5,7,8][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

From R. J. Mathar, Mar 08 2011: (Start)
a(n) = - a(n-1) + a(n-3) + a(n-4) for n>3.
G.f.: (2*x+1)^3 / ( (1-x)*(1+x)*(1+x+x^2) ). (End)
a(n) = (9-cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6))/2. - Wesley Ivan Hurt, Jun 17 2016

A154127 Period 6: repeat [1, 2, 5, 8, 7, 4].

Original entry on oeis.org

1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2, 5, 8, 7, 4, 1, 2

Offset: 0

Paul Curtz, Jan 05 2009

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Cf. A020806, A029898, A070366, A141425, A146501, A153130.

&cat[[1, 2, 5, 8, 7, 4]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

A154127:=n->(27-cos(n*Pi)-20*cos(n*Pi/3)-4*sqrt(3)*sin(n*Pi/3))/6: seq(A154127(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016

Flatten[Table[{1, 2, 5, 8, 7, 4}, {20}]] (* Wesley Ivan Hurt, Jun 17 2016 *)

a(n)=[1,2,5,8,7,4][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

From R. J. Mathar, Feb 25 2009, Mar 09 2009: (Start)
a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.
G.f.: (1+x+3*x^2+4*x^3)/((1-x)*(1+x)*(x^2-x+1)). (End)
a(n) = (27-cos(n*Pi)-20*cos(n*Pi/3)-4*sqrt(3)*sin(n*Pi/3))/6. - Wesley Ivan Hurt, Jun 17 2016

Corrected numerator in g.f R. J. Mathar, Mar 09 2009

A021025 Decimal expansion of 1/21.

Original entry on oeis.org

0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7, 6, 1, 9, 0, 4, 7

Offset: 0

N. J. A. Sloane

			0.047619047...

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1).

Cf. A010701 (1/3), A020806 (1/7).

Join[{0}, RealDigits[10/21, 10, 105][[1]]] (* Alonso del Arte, Mar 07 2019 *)

1/21. \\ Charles R Greathouse IV, Mar 08 2019

A241217 Largest number that when multiplied by 7 produces an n-digit number.

Original entry on oeis.org

1, 14, 142, 1428, 14285, 142857, 1428571, 14285714, 142857142, 1428571428, 14285714285, 142857142857, 1428571428571, 14285714285714, 142857142857142, 1428571428571428, 14285714285714285, 142857142857142857, 1428571428571428571, 14285714285714285714

Offset: 1

J. Lowell, Apr 17 2014

The definition "largest number that when multiplied by 3 produces an n-digit number" gives A002277.

			14*7 = 98 but 15*7 = 105 (too large) so a(2) = 14.

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 34 at p. 62.

Index entries for linear recurrences with constant coefficients, signature (11,-10,-1,11,-10).

Cf. A020806, A002277.

LinearRecurrence[{11,-10,-1,11,-10},{1,14,142,1428,14285},30] (* Harvey P. Dale, Mar 03 2024 *)

a(n) = floor(10^n/7); \\ Michel Marcus, Apr 21 2014

a(n) = floor(10^n/7). - Michel Marcus, Apr 21 2014
G.f.: x*(1+3*x-2*x^2+7*x^3)/((x-1)*(10*x-1)*(x+1)*(x^2-x+1)). - Alois P. Heinz, Apr 30 2014
E.g.f.: (3*cosh(10*x) - 7*cosh(x) + 2*exp(x/2)*(2*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)) - 14*sinh(x) + 3*sinh(10*x))/21. - Stefano Spezia, Jul 31 2024

More terms from Michel Marcus, Apr 21 2014

A021060 Decimal expansion of 1/56.

Original entry on oeis.org

0, 1, 7, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2

Offset: 0

N. J. A. Sloane

Same decimal period as A020806. - R. J. Mathar, Feb 13 2012

			0.017857142857..

Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 1).

Cf. A020806.

Join[{0},RealDigits[1/56,10,120][[1]]] (* or *) PadRight[{0,1,7},120,{1,4,2,8,5,7}] (* Harvey P. Dale, Feb 04 2019 *)

A091720 Babylonian sexagesimal (base 60) expansion of 1/7.

Original entry on oeis.org

8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17, 8, 34, 17

Offset: 0

Jeppe Stig Nielsen, Feb 01 2004

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1).

Cf. A020806, A091721, A091722, A055643.

Cf. A159991. - Reinhard Zumkeller, May 02 2009

RealDigits[ 1/7, 60, 75] [[1]] (* Robert G. Wilson v, Feb 02 2004 *)

A144453 a(n) = A061039(8*n+5).

Original entry on oeis.org

16, 160, 16, 832, 1360, 224, 2800, 3712, 176, 5920, 7216, 320, 10192, 11872, 1520, 15616, 17680, 736, 22192, 24640, 336, 29920, 32752, 3968, 38800, 42016, 560, 48832, 52432, 2080, 60016, 64000, 7568, 72352, 76720, 3008, 85840, 90592, 3536, 100480, 105616

Offset: 0

Paul Curtz, Oct 07 2008

Numerators of 16*(n+1)*(4*n+1)/(9*(8*n+5)^2), so all numbers are multiples of 16 because the denominator is always odd.

Interpreted modulo 9, all numbers from 1 to 8 appear: a(20) is the first entry = 3 (mod 9), a(26) is the first entry = 2 (mod 9), a(80) is the first entry = 6 (mod 9).

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A020806, A141425, A146537.

Numerator[1/9 - 1/(8*Range[0,100] +5)^2] (* G. C. Greubel, Mar 07 2022 *)

[numerator(1/9 - 1/(8*n+5)^2) for n in (0..100)] # G. C. Greubel, Mar 07 2022

a(n) = A061039(8*n+5).

a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81) for n>83. - Colin Barker, Oct 10 2016

Edited and extended by R. J. Mathar, Oct 24 2008

A216606 Decimal expansion of 360/7.

Original entry on oeis.org

5, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7

Offset: 2

Paul Curtz, Sep 10 2012

A020806 preceded by a 5.

Number of degrees in the exterior angle of an equilateral heptagon. Since 1969, used in many (orbiform or Reuleaux) heptagonal coins. Zambia has a natural heptagonal coin. Brazil and Costa Rica have a coin with the natural heptagon inscribed in the coin's disk.

			51.42857...

World of Coins, An Alphabet of Heptagons: Seven-sided Coins.
Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Cf. A019695, A020806, A021018, A060708, A068028, A178817, A178818.

Digits:=100: evalf(360/7); # Wesley Ivan Hurt, Jun 28 2016

Flatten[RealDigits[360/7, 10, 100]] (* Wesley Ivan Hurt, Jun 28 2016 *)

360/7. \\ Charles R Greathouse IV, Sep 12 2012

a(n) = 50 + 10*A020806(n).
After 5, of period 6: repeat [1, 4, 2, 8, 5, 7].
From Wesley Ivan Hurt, Jun 28 2016: (Start)
G.f.: x^3*(5-4*x+3*x^2+3*x^3+2*x^4) / (1-x+x^3-x^4).
a(n) = 9/2 + 11*cos(n*Pi)/6 + 5*cos(n*Pi/3)/3 + sqrt(3)*sin(n*Pi/3), n>2.
a(n) = a(n-1) - a(n-3) + a(n-4) for n>6, a(n) = a(n-6) for n>8. (End)

A021032 Decimal expansion of 1/28.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Same decimal period as A020806. - R. J. Mathar, Feb 13 2011

			0.0357142857142857142857142857142857142857142857...

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Join[{0},RealDigits[1/28,10,98][[1]]] (* Stefano Spezia, Apr 22 2025 *)

cp's OEIS Frontend

A021018 Decimal expansion of 1/14.

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A153110 Period 6: repeat [1, 5, 7, 2, 4, 8].

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A154127 Period 6: repeat [1, 2, 5, 8, 7, 4].

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A021025 Decimal expansion of 1/21.

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A241217 Largest number that when multiplied by 7 produces an n-digit number.

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A021060 Decimal expansion of 1/56.

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A091720 Babylonian sexagesimal (base 60) expansion of 1/7.

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A144453 a(n) = A061039(8*n+5).

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