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 11-17 of 17 results.

A386740 Decimal expansion of the volume of an augmented sphenocorona with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 01 2025

Keywords

Comments

The augmented sphenocorona is Johnson solid J_87.

Examples

			1.7510539003719224011954274331734292512511481527...

Links

Crossrefs

Cf. A010502 (surface area - 1).
Cf. A010507, A020775, A115754, A386739, A386741.

Programs

  • Mathematica
    First[RealDigits[Sqrt[1 + 3*Sqrt[3/2] + Sqrt[13 + Sqrt[54]]]/2 + 1/Sqrt[18], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J87", "Volume"], 10, 100]]

Formula

Equals sqrt(1 + 3*sqrt(3/2) + sqrt(13 + 3*sqrt(6)))/2 + 1/(3*sqrt(2)) = sqrt(1 + 3*A115754 + sqrt(13 + A010507))/2 + A020775.
Equals A386739 + A020775.
Equals the largest real root of 45137758519296*x^16 - 110336743047168*x^14 - 191069246324736*x^12 + 209269081571328*x^10 + 364547659290624*x^8 - 58793017190400*x^6 + 3306865979520*x^4 - 1275399855936*x^2 + 1439671249.

A176051 Decimal expansion of (2+sqrt(6))/2.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 07 2010

Keywords

Comments

Continued fraction expansion of (2+sqrt(6))/2 is A010694.
a(n) = A115754(n) for n > 1; a(1) = 2.

Examples

			(2+sqrt(6))/2 = 2.22474487139158904909...
Note also that (1+sqrt(6))/2 = 1.724744871391589049098642..., the mis-typed golden ratio. - _N. J. A. Sloane_, Jan 19 2025

Crossrefs

Cf. A010464 (decimal expansion of sqrt(6)), A115754 (decimal expansion of sqrt(3/2)), A010694 (repeat 2, 4).
See also A379800.

Programs

  • Mathematica
    RealDigits[(2+Sqrt[6])/2,10,120][[1]]  (* Harvey P. Dale, Apr 21 2011 *)

A068388 Engel expansion of sqrt(3/2).

Original entry on oeis.org

1, 5, 9, 9, 47, 54, 171, 867, 3056, 28687, 133134, 542005, 563497, 1046686, 1955619, 2057281, 42760619, 661780137, 1109113993, 6460565976, 8523453296, 34406061218, 64402180149, 1607033374515, 10943963720662, 124655149151970
Offset: 1

Views

Author

Benoit Cloitre, Mar 03 2002

Keywords

Crossrefs

Cf. A115754, A382713
Cf. A006784.

Programs

  • PARI
    print1(1, ", "); s=(3/2)^(1/2); for(i=0,30,s=s*ceil(1/s)-1; print1(ceil(1/s),", "));

A171547 Decimal expansion of sqrt(3/14).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Dec 11 2009

Keywords

Comments

The absolute value of the Clebsch-Gordan coupling coefficient = <2 2 ; -2 0 | 4 -2>.

Examples

			sqrt(3/14) = sqrt(42)/14 = 0.462910049886275730783283388291999761264...

Links

Crossrefs

Cf. A002194, A010471, A115754, A010465, A171537, A002193.

Programs

  • Mathematica
    RealDigits[Sqrt[3/14],10,120][[1]] (* Harvey P. Dale, Sep 23 2011 *)

Formula

Equals A002194/A010471 = A115754/A010465 = A171537/A002193.

A188924 Decimal expansion of sqrt(4+sqrt(15)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Apr 13 2011

Keywords

Comments

Decimal expansion of the length/width ratio of a sqrt(6)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.
A sqrt(6)-extension rectangle matches the continued fraction [2,1,4,6,1,1,2,25,3,...] for the shape L/W=sqrt(4+sqrt(15)). This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...]. Specifically, for the sqrt(6)-extension rectangle, 2 squares are removed first, then 1 square, then 4 squares, then 6 squares,..., so that the original rectangle of shape sqrt(4+sqrt(15)) is partitioned into an infinite collection of squares.

Examples

			2.8058837014757787150980888095693049628427513...

Crossrefs

Cf. A020797, A115754, A188925.

Programs

  • Mathematica
    r = 6^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
  • PARI
    sqrt(3/2) + sqrt(5/2) \\ Hugo Pfoertner, Feb 20 2024

Formula

Equals A115754 + 10*A020797. - Hugo Pfoertner, Feb 20 2024

A022772 Ordered sequence of distinct terms of the form floor(x^i * floor(x^j)), i,j >= 0, where x = sqrt(3/2).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 41, 43, 45, 46, 47, 51, 53, 55, 56, 57, 62, 65, 67, 68, 69, 70, 76, 79, 80, 82, 83, 84, 85, 86, 94, 97, 98, 101, 102, 103, 104, 105, 115, 119
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A115754 (sqrt(3/2)).

Extensions

Offset corrected by Sean A. Irvine, May 21 2019

A179461 Decimal expansion of sqrt(51)/7.

Original entry on oeis.org

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

Views

Author

Mark Dols, Jul 14 2010

Keywords

Comments

sqrt(3/2)= sqrt(12/8)= 1.224744... sqrt(51/49)= sqrt(102/98)= 1.0202040612... sqrt (501/499)=sqrt (1002/998)= 1.002002004...

Crossrefs

Cf. A063886, A115754, A000984, A151821.

Programs

Extensions

Keyword:frac replaced by keyword:cons - R. J. Mathar, Jul 20 2010
More terms from Robert G. Wilson v, Aug 23 2010
Previous Showing 11-17 of 17 results.

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