Somos sequences
Nelson Stephens
Goldsmiths
A Somos 4 sequence of rational numbers can be defined by quadratic
recursion:
h_(k+2)*h_(k-2) = a*h_(k+1)*h_(k-1) + b*(h_k)^2.
For example, with a = b = 1 and h_1 = h_2 = h_3 = h_4 = 1, the sequence
is a
sequence of integers:
1, 1, 1, 1, 2, 3, 7, 23, 59, 314, ...
The talk will consider:
the work of Shipsey, Swart and others on these sequences and their
relation to elliptic divisibility sequences;
Somos 5 sequences;
generation of primes using Somos and elliptic divisibility sequences;
'realisability' of such sequences.