%I A111693
%S A111693 3,11,29,53,83,127,173,227,293,367,443
%N A111693 The number system may be represented by linearly stringing together all 
               the square domains. The number of the domain is given by r. it is 
               noted that this has the same value as the circuit number in the Ellerstein 
               square spiral. One below each odd square is a zero centered octagonal 
               number, which is divisible by 8. The value of this is eight times 
               a triangle number. It may be seen that there are r octades in each 
               square domain. The sequence is the first prime number in the first 
               octade of each square domain.
%C A111693 Other work is in progress where the distribution of primes in successive 
               octads is being calculated to see what pattern if any emerges. These 
               will be published when they are available. It is noted that each 
               square domain has 8 sectors of length r besides the r octades of 
               length 8 which are intertwined.
%D A111693 Stuart M. Ellerstein, J. Recreational Mathematics, Vol. 29,3, pp. 188 
               - 189,1998. Stuart M. Ellerstein, J. Recreational Mathematics, Vol. 
               30,4, pp. 246 - 250,1999- 2000.
%e A111693 For the sixth square domain r=6. The ZCON is 120, which is 8x15, since 
               it is
%e A111693 8x 6(6-1)/2 and the first prime is 8x15 + 7. The odd square is (2r -1)^2 
               = 121.
%Y A111693 Sequence in context: A018743 A077279 A111227 this_sequence A100032 A069350 
               A053845
%Y A111693 Adjacent sequences: A111690 A111691 A111692 this_sequence A111694 A111695 
               A111696
%K A111693 easy,nonn,uned
%O A111693 0,1
%A A111693 Stuart M. Ellerstein (ellerstein(AT)aol.com), Jun 17 2006