cp's OEIS Frontend

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).

%I A160772 #14 Sep 08 2022 08:45:45
%S A160772 13,31,91,133,241,307,463,757,871,1261,1561,1723,2071,2653,3307,3541,
%T A160772 4291,4831,5113,6007,6643,7657,9121,9901,10303,11131,11557,12433,
%U A160772 15751,16771,18361,18907,21757,22351,24181,26083,27391,29413,31507,32221,35911,36673
%N 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).
%C A160772 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.
%D A160772 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).
%D A160772 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).
%D A160772 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).
%H A160772 G. C. Greubel, <a href="/A160772/b160772.txt">Table of n, a(n) for n = 3..10000</a>
%F A160772 a(n) = (prime(n)-2)*(prime(n)-1) + 1.
%e A160772 For prime(3) = 5: a(n) = (3)(4)+1 = 13; for prime(4) = 7: a(n) = (5)(6)+1 = 31
%t A160772 Table[(Prime[n] - 2) (Prime[n] - 1) + 1, {n, 3, 50}] (* _T. D. Noe_, Dec 30 2012 *)
%o A160772 (PARI) for(n=3, 50, print1((prime(n)-2)*(prime(n)-1) + 1, ", ")) \\ _G. C. Greubel_, Apr 26 2018
%o A160772 (Magma) [(NthPrime(n)-2)*(NthPrime(n)-1) + 1: n in [3..30]]; // _G. C. Greubel_, Apr 26 2018
%Y A160772 Cf. A128929, A040976.
%K A160772 nonn
%O A160772 3,1
%A A160772 _Aminu Alhaji Ibrahim_, Jun 09 2009
%E A160772 Terms changed by _T. D. Noe_, Dec 30 2012