[seqfan] turtle product
primeness at borve.org
Tue Dec 10 17:41:12 CET 2013
Noting that the set of turtle transforms is equivalent to the set of
integer sequences, we can define the (non-commutative) turtle product of
two integer sequences a(n) and b(n) as the sequence of Gaussian integers
a(n)#b(n) := c(n) = sum from 1 to n of a(n)*i^(b(n)).
Then the sequence
c(n) := sum from k=1 to n of pi(k)*i^(k(k-1)/2)
plotted at <http://borve.org/plots/1000.jpg>
can be called the turtle product of the primes and the triangular
numbers, with the latter starting at 0.
Plot of (primes)#(Fibonaccis):
This gives rise to questions such as:
what sequences commute with the primes?
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