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 1-4 of 4 results.

A100264 Decimal expansion of a non-random Chaitin's constant.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Nov 10 2004

Keywords

Examples

			0.00787499699...

References

  • G. Chaitin, Meta Math!:The Quest for Omega, Pantheon Books NY 2005.

Links

Crossrefs

Cf. A079365.

A133248 Provides a relationship between a representation of Lisp programs of length n and Chaitan's Omega: If[A124027(n)==0, then row sum of[A124027].

Original entry on oeis.org

9, 5798, 2356779, 6536382
Offset: 1

Views

Author

Roger L. Bagula, Oct 14 2007

Keywords

Comments

If the first two rows of A124027 are left off, the wrong answer is given for the number of program representations necessary to be tested. My machine won't calculate to the next one at n=25. This line of reasoning also produces the sequence: Flatten[Table[If[c[[n]] == 1, n, {}], {n, 1, Length[c]}]] {7, 14, 20, 21, 25, 30, 31, 33, 37, 38, 39, 40, 41, 42, 45, 47, 48, 49, 51, 52, 53, 55, 60}

Crossrefs

Cf. A079365, A124027.

Programs

  • Mathematica
    (*A079365*); c = {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1,1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0,1, 0, 0, 0, 0, 1, 0, 0, 0, 0}; (*A124027*); p[0, x] = 0; p[1, x] = x; p[2, x] = 1; p[k_, x_] := p[k, x] = Sum[ p[j, x]*p[k - j, x], {j, 2, k - 1}]; Flatten[Table[If[c[[n + 1]] == 1, Sum[CoefficientList[p[n, x], x][[m]], {m, 1, Length[CoefficientList[p[n, x], x]]}], {}], {n, 0, 21}] ]

Formula

a(n) = If[A124027(m)==0, then row sum of[A124027](m)

A133249 Location of ones in the binary representation of Chaitan's Omega: If[A124027(n)==0, then n.

Original entry on oeis.org

7, 14, 20, 21, 25, 30, 31, 33, 37, 38, 39, 40, 41, 42, 45, 47, 48, 49, 51, 52, 53, 55, 60
Offset: 1

Views

Author

Roger L. Bagula, Oct 14 2007

Keywords

Crossrefs

Cf. A079365, A124027.

Programs

  • Mathematica
    (*A079365*); c = {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1,1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0,1, 0, 0, 0, 0, 1, 0, 0, 0, 0}; Flatten[Table[If[c[[n]] == 1, n, {}], {n, 1, Length[c]}]]

Formula

a(n) = If[A124027(m)==0, then (m)

A160753 Binary expansion of the Chaitin halting probability Omega_L for a certain programming language L.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0
Offset: 0

Views

Author

N. J. A. Sloane, Jan 29 2010

Keywords

Comments

If this sequence were extended to 5000 terms, it would settle the Riemann hypothesis.

References

  • C. S. Calude, E. Calude and M. J. Dinneen, A new measure of the difficulty of problems, J. Mult.-Valued Logic Soft. Comput., 12 (2006), 285-307.
  • C. S. Calude and M. J. Dinneen, Exact approximations of omega numbers, Internat. J. Bifur. Chaos, 17 (6) (2007), 1937-1954.

Links

Crossrefs

Cf. A079365.
Showing 1-4 of 4 results.

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

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