A291293 - OEIS

%I #17 Oct 23 2018 02:38:36

%S 2,3,2,0,0,2,0,0,3,1,1,3,1,1,2,2,4,4,0,0,1,3,4,2,0,3,2,4,0,1,3,3,1,3,

%T 0,2,4,2,4,1,2,3,1,3,0,2,1,2,1,0,3,3,0,0,0,4,4,4,3,1,2,1,2,1,1,2,3,2,

%U 1,1,0,3,1,1,4,2,3,4,1,4,3,3,1,3,0

%N Sequence mod 5 defined by Baldini-Eschgfäller coupled dynamical system (f,lambda,alpha) with f(k) = A000203(k)-1, lambda(y) = 3y+2 mod 5 for y in Y = {0,1,2,3,4}, and alpha(k) = k mod 5 for k in Omega = {primes}.

%C This sequence assumes that the Erdos conjecture is true, that iterating k -> sigma(k)-1 always reaches a prime (cf. A039654).

%H Lucilla Baldini, Josef Eschgfäller, <a href="http://arxiv.org/abs/1609.01750">Random functions from coupled dynamical systems</a>, arXiv preprint arXiv:1609.01750 [math.CO], 2016. See Example 3.6.

%F Let f(k) = A000203(k)-1 = sigma(k) - 1, lambda(y) = 3y+2 mod 5 for y in Y = {0,1,2,3,4}, and alpha(k) = k mod 5 for k in Omega = {primes}. Here sigma is the sum of divisors function A000203.

%F Then a(n) for n >= 2 is defined by a(n) = alpha(n) if n in Omega, and otherwise by a(n) = lambda(a(f(n))).

%Y Cf. A000203, A039654, A291291, A262684.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Aug 30 2017