cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-18 of 18 results.

A177157 Decimal expansion of sqrt(221).

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, May 03 2010

Keywords

Comments

Continued fraction expansion of sqrt(221) is A040206.

Examples

			sqrt(221) = 14.86606874731850552261...

Crossrefs

Cf. A010470 (decimal expansion of sqrt(13)), A010473 (decimal expansion of sqrt(17)), A177156 (decimal expansion of (9+sqrt(221))/14), A040206 (14 followed by (repeat 1, 6, 2, 6, 1, 28)).

A017955 Powers of sqrt(17) rounded down.

Original entry on oeis.org

1, 4, 17, 70, 289, 1191, 4913, 20256, 83521, 344365, 1419857, 5854220, 24137569, 99521746, 410338673, 1691869691, 6975757441, 28761784747, 118587876497, 488950340714, 2015993900449, 8312155792152, 34271896307633, 141306648466586, 582622237229761, 2402213023931974
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A000196, A001026 (even bisection), A010473 (sqrt(17)).

Programs

Formula

a(n) = floor(sqrt(17^n)) = A000196(A001026(n)). - Vincenzo Librandi, Jun 24 2011

A177345 Decimal expansion of sqrt(2805).

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, May 06 2010

Keywords

Comments

Continued fraction expansion of sqrt(2805) is 52 followed by (repeat 1, 25, 2, 25, 1, 104).
sqrt(2805) = sqrt(3)*sqrt(5)*sqrt(11)*sqrt(17).

Examples

			sqrt(2805) = 52.96225070746144187131...

Crossrefs

Cf. A002194 (decimal expansion of sqrt(3)), A002163 (decimal expansion of sqrt(5)), A010468 (decimal expansion of sqrt(11)), A010473 (decimal expansion of sqrt(17)), A177344 (decimal expansion of (33+sqrt(2805))/66).

A380895 Decimal expansion of (sqrt(17) + 1)/(4*sqrt(17)).

Original entry on oeis.org

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

Views

Author

Stefano Spezia, Feb 07 2025

Keywords

Comments

This constant and A380896 give the stationary distribution for maximal entropy random walk on the barred-square graph (see Burda et al.).

Examples

			0.310633906259083243379726615529030544487458812...

Links

Crossrefs

Cf. A010473, A222132, A380896.

Programs

  • Mathematica
    RealDigits[(Sqrt[17]+1)/(4Sqrt[17]),10,100][[1]]
  • PARI
    1/4+1/sqrt(272) \\ Charles R Greathouse IV, Feb 08 2025

Formula

Equals 1/2 - A380896.
Minimal polynomial: 34*x^2 - 17*x + 2. - Stefano Spezia, Aug 03 2025

A380896 Decimal expansion of (sqrt(17) - 1)/(4*sqrt(17)).

Original entry on oeis.org

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

Views

Author

Stefano Spezia, Feb 07 2025

Keywords

Comments

A380895 and this constant give the stationary distribution for maximal entropy random walk on the barred-square graph (see Burda et al.).

Examples

			0.18936609374091675662027338447096945551254118786...

Links

Crossrefs

Cf. A010473, A222132, A380895.

Programs

  • Mathematica
    RealDigits[(Sqrt[17]-1)/(4Sqrt[17]),10,100][[1]]
  • PARI
    1/4-1/sqrt(272) \\ Charles R Greathouse IV, Feb 08 2025

Formula

Equals 1/2 - A380895.
Minimal polynomial: 34*x^2 - 17*x + 2. - Stefano Spezia, Aug 03 2025

A358945 Decimal expansion of the positive root of 4*x^2 + x - 1.

Original entry on oeis.org

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

Views

Author

Wolfdieter Lang, Jan 20 2023

Keywords

Comments

The negative root is -(A189038 - 1) = -0.6403882032... .
c^n = A052923(-n) + A006131(-(n+1))*phi17, for n >= 0, with phi17 = A222132 = (1 + sqrt(17))/2, A052923(-n) = -(-2*i)^(-n)*S(-(n+2), i/2) = (i/2)^n*S(n, i/2), with i = sqrt(-1), and A006131(-(n+1)) = A052923(-n+1)/4 = -(i/2)^(n+1)*S(n-1, i/2), with the S-Chebyshev polynomials (see A049310), and S(-n, x) = -S(n-2, x), for n >= 1. - Wolfdieter Lang, Jan 04 2024

Examples

			c = 0.39038820320220756872767623199675962814339990317170255429982919663...

Links

Crossrefs

Cf. A006131, A010473, A049310, A052923, A174930, A189038, A222132.

Programs

  • Mathematica
    RealDigits[(Sqrt[17] - 1)/8, 10, 120][[1]] (* Amiram Eldar, Jan 20 2023 *)
RealDigits[Root[4x^2+x-1,2],10,120][[1]] (* Harvey P. Dale, Jan 15 2024 *)

Formula

c = (-1 + sqrt(17))/8 = A189038 - 5/4 = A174930 - 5/8.
c = 1/phi17 = (-1 + phi17)/4, with phi17 = A222132. - Wolfdieter Lang, Jan 05 2024

A370393 Decimal expansion of the area of a unit heptadecagon (17-gon).

Original entry on oeis.org

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

Views

Author

Michal Paulovic, Feb 17 2024

Keywords

Comments

This constant multiplied by the square of the side length of a regular heptadecagon equals the area of that heptadecagon.
17^2 divided by this constant equals 68 * tan(Pi/17) = 12.71140300... which is the perimeter and the area of an equable heptadecagon with its side length 4 * tan(Pi/17) = 0.74772958... .
An equable rectangle with its perimeter and area = 17 has side lengths:
a = s^2/8 = (17 - sqrt(17)) / 4 = (17 - A010473) / 4 = 3.21922359...
b = 136/s^2 = (17 + sqrt(17)) / 4 = (17 + A010473) / 4 = 5.28077640...
where s is the parameter from the formula mentioned below.

Examples

			22.7354918984165514...

Links

Crossrefs

Cf. A007450, A010473, A019684 (Pi/17), A210644 (cos(2*Pi/17)), A210649, A228787, A241243, A329592, A343061.

Programs

  • Maple
    evalf(17 / (4 * tan(Pi/17)), 100);
  • Mathematica
    RealDigits[17 / (4 * Tan[Pi/17]), 10, 100][[1]]
  • PARI
    17 / (4 * tan(Pi/17))

Formula

Equals 17 / (4 * tan(Pi/17)) = 17 / (4 * A343061).
Equals 1 / (4 * A007450 * A343061).
Equals 17 * cos(Pi/17) / (4 * sin(Pi/17)).
Equals 17 * A210649 / (4 * A241243).
Equals 17 * A210649 / (2 * A228787).
Equals 17 * cot(Pi/17) / 4.
Equals 17 * sqrt(4 / (s^2 - 2 * s - 4 * sqrt(17 + 3 * sqrt(17) - s - sqrt(17) * 16/s)) - 1/16) where s = sqrt(34 - 2 * sqrt(17)) = 4 * A329592.
The minimal polynomial is 4294967296*x^16 - 3103113871360*x^14 + 510054948143104*x^12 - 28954726431195136*x^10 + 653743432704327680*x^8 - 6011468019822067712*x^6 + 20881180982314634240*x^4 - 21552361799603318912*x^2 + 2862423051509815793.

A377968 Decimal expansion of tan(arctan(4)/4).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 13 2024

Keywords

Examples

			0.34415073140891080771475922788534684760565020832584...

Links

Crossrefs

Cf. A010473, A019684, A195628.

Programs

  • Mathematica
    First[RealDigits[Tan[ArcTan[4]/4], 10, 100]]

Formula

Equals 2*(cos(6*Pi/17) + cos(10*Pi/17)) = 2*(cos(6*A019684) + cos(10*A019684)).
Equals (sqrt(34 + 2*sqrt(17)) - sqrt(17) - 1)/4 = (sqrt(34 + 2*A010473) - A010473 - 1)/4.
Equals the root closest to 0 of x^4 + x^3 - 6*x^2 - x + 1.
Previous Showing 11-18 of 18 results.

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