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 1-3 of 3 results.

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

A084256 Decimal expansion of x such that x^2 + x^3 + x^5 + x^7 + x^11 + x^13 + x^17 + ... = 1.

Original entry on oeis.org

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

Views

Author

Frank Ellermann, May 23 2003

Keywords

Comments

A constant appearing in the asymptotic formula for the number of prime additive compositions. See Finch's article.

Examples

			0.67740177613066042797630631643196719199252141284...

Links

Crossrefs

Cf. A000040, A084255, A084257.

Programs

  • Mathematica
    RealDigits[x/.FindRoot[1==Sum[x^Prime[n], {n, 150}], {x, {0, 1}}, WorkingPrecision->100]][[1]] (* T. D. Noe, Oct 14 2003 *)

Extensions

More terms from T. D. Noe, Oct 14 2003

A193743 Decimal expansion of the only positive real solution to x^2/2! - x^3/3! + x^5/5! - x^7/7! + x^11/11! - ... = 0, using the prime numbers (2, 3, 5, 7 ...)

Original entry on oeis.org

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

Views

Author

Kausthub Gudipati, Aug 03 2011

Keywords

Comments

The constant is 5. 8154599887 2232829407 3007970995 6593490083 3301145...

Links

Crossrefs

Cf. A078756, A084257
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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