A380340 a(n) = phi(1 + phi(2 + phi(3 + ... phi(n)))).

1, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Author

Michel Marcus, Jan 22 2025

Keywords

• nonn
• easy

Links

• Luis Palacios Vela and Christian Wolird, The Forestry of Adversarial Totient Iterations, arXiv:2501.10616 [math.NT], 2025.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A000010, A132857, A380341, A380342, A380354, A380414, A380415.

Programs

Mathematica

PadRight[{1, 1, 2, 2}, 100, 4] (* Paolo Xausa, Jan 22 2025 *)

PARI

a(n) = my(x=0); forstep(k=n, 1, -1, x = eulerphi(x+k)); x;

Python

from functools import reduce
from sympy import totient
def A380340(n): return reduce(lambda x,y:totient(x)+y,range(n,-1,-1)) # Chai Wah Wu, Jan 22 2025

Formula

a(n) = 4 for n >= 5 (see Vela and Wolird). - Paolo Xausa, Jan 22 2025

G.f.: x*(2*x^4+x^2+1)/(1-x). - Alois P. Heinz, Jan 22 2025