|
| |
|
|
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).
|
|
1
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
3,1
|
|
|
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.
|
|
|
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
|
|
|
|
FORMULA
|
a(n) = (prime(n)-2)*(prime(n)-1) + 1.
|
|
|
EXAMPLE
|
For prime(3) = 5: a(n) = (3)(4)+1 = 13; for prime(4) = 7: a(n) = (5)(6)+1 = 31
|
|
|
MATHEMATICA
|
Table[(Prime[n] - 2) (Prime[n] - 1) + 1, {n, 3, 50}] (* T. D. Noe, Dec 30 2012 *)
|
|
|
PROG
|
(PARI) for(n=3, 50, print1((prime(n)-2)*(prime(n)-1) + 1, ", ")) \\ G. C. Greubel, Apr 26 2018
(Magma) [(NthPrime(n)-2)*(NthPrime(n)-1) + 1: n in [3..30]]; // G. C. Greubel, Apr 26 2018
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
