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.

A160772 Number of nodes (or order) of a graph model obtained using an automata scheme on sets of order prime(n) >= 5 and in which all not halt states are linked by arcs (edges).

Original entry on oeis.org

13, 31, 91, 133, 241, 307, 463, 757, 871, 1261, 1561, 1723, 2071, 2653, 3307, 3541, 4291, 4831, 5113, 6007, 6643, 7657, 9121, 9901, 10303, 11131, 11557, 12433, 15751, 16771, 18361, 18907, 21757, 22351, 24181, 26083, 27391, 29413, 31507, 32221, 35911, 36673
Offset: 3

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Author

Aminu Alhaji Ibrahim, Jun 09 2009

Keywords

Comments

Special graph models were constructed (Ibrahim, 2009) using an automata scheme involving some transition function defined on the Special (123)-avoiding permutation patterns reported by Ibrahim and Audu (2005; Ibrahim, 2008). The order of these special variety of graph models represents an improvement of the earlier models (Ibrahim 2008) in the study of the degree/diameter problems as used in circuit designs and analysis. The sequence represents the number of nodes (order) in this latest variety of graph models for primes >= 5.

Examples

			For prime(3) = 5: a(n) = (3)(4)+1 = 13; for prime(4) = 7: a(n) = (5)(6)+1 = 31

References

  • A. A. Ibrahim, Some Transformation Schemes Involving the Special (132) - avoiding Permutation Patterns and a Binary Coding: An Algorithmic Approach Asian Journal of Algebra 1 (1):10-14, Asian Network for Scientific Information (ANSI), Pakistan (2008).
  • A. A. Ibrahim and M. S. Audu, Some Group theoretic Properties of Certain Class of (123) and (132)-Avoiding Patterns Numbers: an enumeration scheme, African journal Natural Sciences Vol. 8: 79-84 (2005).
  • A. A. Ibrahim, and M. S. Audu, On Stable Variety of Cayley Graphs For Efficient Interconnection Networks Proceedings of Annual National Conference of Mathematical Association of Nigeria (MAN) held at Federal College of Education Technical, Gusau 26th- 30th August, 2008:156-161 (2008).

Links

Crossrefs

Cf. A128929, A040976.

Programs

  • Magma
    [(NthPrime(n)-2)*(NthPrime(n)-1) + 1: n in [3..30]]; // G. C. Greubel, Apr 26 2018
  • Mathematica
    Table[(Prime[n] - 2) (Prime[n] - 1) + 1, {n, 3, 50}] (* T. D. Noe, Dec 30 2012 *)
  • PARI
    for(n=3, 50, print1((prime(n)-2)*(prime(n)-1) + 1, ", ")) \\ G. C. Greubel, Apr 26 2018

Formula

a(n) = (prime(n)-2)*(prime(n)-1) + 1.

Extensions

Terms changed by T. D. Noe, Dec 30 2012

A128984 Degree of the special subgraph of Cayley graph constructed using the special (123)-avoiding and (132)-avoiding permutation patterns as generators.

Original entry on oeis.org

2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 50, 52, 56, 58, 60, 66, 70, 72, 76, 78, 82, 86, 88, 90, 96, 100, 102, 106, 110, 112, 116, 118, 122, 128, 130, 136, 140, 142, 146, 148, 150, 156, 160, 166, 170, 172, 178, 180, 182, 186, 190, 192, 196, 198, 200, 202
Offset: 3

Views

Author

Aminu Alhaji Ibrahim, Apr 30 2007

Keywords

Comments

This sequence is constructed using a special veriety of subgraphs of Cayley graphs in order for a study of the degree/diameter problem.

References

  • Ibrahim A.A. and Audu M.S.(2005) Some Group Theoretic Properties of Certain Class of (123) and (132)-Avoiding Patterns of Numbers: An Enumeration Scheme: An enumeration Scheme, African Journal of Natural Sciences, Vol. 8:79-84
  • Ibrahim A.A. (2006) A Counting Scheme And Some Algebraic Properties of A Class of Special Permutation Patterns. (in preparation)
  • Ibrahim A.A. (2005) On the Combinatorics of Succession In A 5-element Sample Abacus Journal of Mathematical Association of Nigeria Vol. 32, No. 2B:410-415

Crossrefs

Cf. A123642, A128929.

Formula

Recursion relation:f(0)=2, f(2)=4, f(3)=6, f(4)=12, f(5)=f(1)+f(2)+f(3)+f(4)/f(0), f(n)=f(n-1)+f(n-2)+f(n-3)+f(n-4)-f(n-5)/f(0)-f(n-5), n>5 and provided the difference between consecutive numbers (before and at the start of the addition) does not exceed four digits. If however, this difference (m-(m-1)<=4 the f(n)=f(n-1)+f(n-2)+f(n-3)+f(n-4)/f(0)-f(n-4). [Indices need to be changed to match the offset. - R. J. Mathar, Dec 04 2011]

Extensions

An obviously incorrect prime formula deleted. - R. J. Mathar, Dec 04 2011

A144075 Duplicate of A008621.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21
Offset: 1

Views

Author

Eric W. Weisstein, Sep 09 2008

Keywords

Links

Crossrefs

Cf. A002265, A128929.

Programs

  • Mathematica
    Ceiling[(n+1)/4]

Formula

G.f.: x(1+x^3-x^4)/((1-x)^2(1+x)(1+x^2)). - R. J. Mathar, Sep 12 2008
Showing 1-3 of 3 results.

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