A291293 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}.

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, 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, 1, 1, 0, 3, 1, 1, 4, 2, 3, 4, 1, 4, 3, 3, 1, 3, 0

Offset: 2

Author

N. J. A. Sloane, Aug 30 2017

Keywords

• nonn

Comments

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

Links

• Lucilla Baldini, Josef Eschgfäller, Random functions from coupled dynamical systems, arXiv preprint arXiv:1609.01750 [math.CO], 2016. See Example 3.6.

Crossrefs

Cf. A000203, A039654, A291291, A262684.

Formula

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.

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))).