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 11-16 of 16 results.

A152062 Decimal expansion of number with continued fraction expansion 1, 2, 3, 5, 7, 11, 13, 17, 19, ...

Original entry on oeis.org

1, 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
Offset: 1

Views

Author

Frank S. Thomas (fthomas(AT)physik.uni-wuerzburg.de), Nov 22 2008

Keywords

Examples

			1.4323320871859028689092537...

Crossrefs

Cf. A064442, A127549.

Programs

  • Mathematica
    RealDigits[N[FromContinuedFraction[Prepend[Table[Prime[n], {n, 1, 100}], 1]], 100]][[1]]

Formula

One plus A084255. [R. J. Mathar, Nov 27 2008]
Equals 1+1/(2+1/(3+1/(5+1/(7+1/(11+...))))). - Daniel Forgues, Mar 08 2016

A108170 Decimal expansion of the number 5.1413105308627310489... having continued fraction expansion 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, ... (greater of twin primes A006512).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Apr 20 2007

Keywords

Crossrefs

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

Programs

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

Extensions

a(99)-a(100) corrected by Sean A. Irvine, Jul 09 2023

A229911 Decimal expansion of number whose continued fraction expansion is formed by the difference of consecutive primes (A001223).

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 03 2013

Keywords

Examples

			1.408248346018747844183196249564... = [1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, ...]

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 157.

Links

Crossrefs

Cf. A001223, A064442.

Programs

  • Maple
    P:=proc(q) local a,n,v; v:=array(1..q); a:=1;
for n from 1 to q do v[n]:=(ithprime(n+1)-ithprime(n)); od;
for n from q by -1 to 1 do a:=v[n]+1/a; od; print(evalf(a,200));
end: P(10^4);
  • Mathematica
    m=200;RealDigits[FromContinuedFraction[Differences[Prime[Range[1001]]]],10,m][[1]] (* Zak Seidov, Oct 04 2013 *)
  • PARI
    diff(v)=vector(#v-1,i,v[i+1]-v[i])
(M->M[1,1]/M[2,1]*1.)(contfracpnqn(diff(primes(100)))) \\ Charles R Greathouse IV, Oct 04 2013

A261827 Decimal expansion of the number whose continued fraction expansion consists of the perfect numbers (A000396).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Sep 02 2015

Keywords

Examples

			6.0357117143069233346283990529260946180806175748136895461...

Links

Crossrefs

Cf. A000396, A073821, A073822, A073823, A073824, A052119, A064442.

Programs

  • Mathematica
    ind = {1, 2, 3, 4, 6, 7, 8, 11, 18, 24, 28, 31, 98, 111} (* from A016027 *); p = Prime@ ind; pn = (2^p - 1)(2^(p - 1)); RealDigits[ FromContinuedFraction@ pn, 10, 111][[1]] (* Robert G. Wilson v, Sep 13 2015 *)

A328726 Decimal expansion of the number with continued fraction expansion 4, 6, 8, 9, 10, 12, 14, 15, ... (A002808 = composite numbers).

Original entry on oeis.org

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

Views

Author

Alexander Victorius Budianto, Oct 26 2019

Keywords

Examples

			4.163310470941149346202768593813039507043958...

Crossrefs

Cf. A002808, A060997, A064442, A084255, A127551, A302937.

Formula

Equals 1/A302937. - Alois P. Heinz, Nov 13 2019

Extensions

More digits from Alois P. Heinz, Nov 13 2019

A330867 Decimal expansion of the continued fraction 1/(1 + 2/(2 + 3/(3 + 5/(5 + 7/(7 + ... + prime(k)/(prime(k) + ...)))))).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 28 2020

Keywords

Examples

			0.58152500459221465439915170481800446195586754...

Links

Crossrefs

Cf. A000040, A064442, A068996, A073333, A084255, A085825, A152062, A191504, A191815, A233588, A247856.
Previous Showing 11-16 of 16 results.

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