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.

Showing 1-10 of 16 results. Next

A127549 Decimal expansion of the number 1.31303673643358290638395160264... having continued fraction expansion 1, 3, 5, 7, 11, 13, 17, 19, ...

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Examples

			1.3130367364335829063839516026417824763966897718032563402101244421445...

Crossrefs

Cf. A064442.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, Prime[n]], {n, 2, 100}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]
RealDigits[FromContinuedFraction[Join[{1},Prime[Range[2,5000]]]],10,100][[1]] (* Harvey P. Dale, Jul 27 2017 *)

Extensions

One digit corrected by Harvey P. Dale, Jul 27 2017

A127551 Decimal expansion of the number 5.1410381418412742236797378119983... having continued fraction expansion 5, 7, 11, 13, 17, 19, ... (successive odd primes starting from 5).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Examples

			5.1410381418412742236797378119983174092833067391135342072110210562...

Crossrefs

Cf. A064442, A127549, A127551, A127552, A127553, A127555.

Programs

  • Mathematica
    a = {}; Do[AppendTo[a, Prime[n]], {n, 3, 100}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]
RealDigits[ FromContinuedFraction[Prime /@ Range[3, 50]], 10, 111][[1]]

Extensions

More terms from Robert G. Wilson v, Dec 30 2007

A084255 Decimal expansion of continued fraction 1/(2+1/(3+1/(5+1/(7+1/(11+...))))).

Original entry on oeis.org

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

Views

Author

Frank Ellermann, May 23 2003

Keywords

Comments

Decimal expansion of the constant whose continued fraction form is the sequence of all the prime numbers.

Examples

			0.4323320871859028689...

Links

Crossrefs

Cf. A000040, A084256, A084257, A152062

Programs

  • Mathematica
    RealDigits[1/FromContinuedFraction@ Prime@ Range@ 34, 10, 111] (* or *)
RealDigits[ Fold[1/(#1 + #2) &, 1, Reverse@ Prime@ Range@35], 10, 111] (* Robert G. Wilson v, Dec 26 2016 *)

Formula

1/A064442. - Franklin T. Adams-Watters, Jul 31 2009

A127552 Decimal expansion of the number 3.19644719338616871113868629540207517... having continued fraction expansion 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, ... (lesser of twin primes A001359).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127553, A127555.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[Prime[n] + 2], AppendTo[a, Prime[n]]], {n, 2, 500}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]

Extensions

a(100) corrected by Sean A. Irvine, Jul 09 2023

A127555 Decimal expansion of the number 4.164393920313549053413239828743... having continued fraction expansion 4, 6, 12, 18, 30, 42, 60, 72, 102, ... (averages of twin primes A014574).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127556, A127557, A127558, A127559.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[Prime[n] + 2], AppendTo[a, Prime[n] + 1]], {n, 2, 500}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]

A127550 Decimal expansion of the number 3.19451324273619331289098105345... having continued fraction expansion 3, 5, 7, 11, 13, 17, 19, ... (successive odd primes).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127551, A127552, A127553, A127555.

Programs

  • Mathematica
    a = {}; Do[AppendTo[a, Prime[n]], {n, 2, 100}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]
RealDigits[FromContinuedFraction[Prime[Range[2,40]]],10,120][[1]] (* Harvey P. Dale, Mar 25 2012 *)

A127556 Decimal expansion of the number 4.1636635147332912770473687837946011358... having continued fraction expansion 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, ... (arithmetical average of two consecutive odd primes A024675).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127558, A127559, A024675.

Programs

  • Mathematica
    a = {}; Do[AppendTo[a, (Prime[n] + Prime[n + 1])/2], {n, 2, 500}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]

Extensions

a(100) corrected by Sean A. Irvine, Jul 09 2023

A127557 Decimal expansion of the number 5.018865657377378233714156283... having continued fraction expansion 5, 53, 157, 173, 211, 257, 263, 373, 563, ... (balanced primes order one A006562).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127558, A127559, A006562.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 1000}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]

A127559 Decimal expansion of the number 734.000353982279850297391846... having continued fraction expansion 734, 2825, 5957, 10305, 13932, ... (interprimes of third order A126556).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127558, A127559, A126555, A126556.

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009

A127558 Decimal expansion of the number 29.000694926917980144237135814... having continued fraction expansion 29, 1439, 4211, 7703, 12907, 14957, ... (A126555).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127559, A126555.

Programs

  • Mathematica
    b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 100000}];Do[If[PrimeQ[(a[[k + 1]] + a[[k]])/2], AppendTo[b, (a[[k + 1]] + a[[k]])/2]], {k, 1, Length[a] - 1}]; RealDigits[N[FromContinuedFraction[b], 100]][[1]]

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009
Showing 1-10 of 16 results. Next

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