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

1,3

Links

Table of n, a(n) for n=1..89.

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).

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A065285 A302437 A179932 * A267649 A071805 A063511

Adjacent sequences: A380337 A380338 A380339 * A380341 A380342 A380343

Keyword

nonn,easy

Author

Michel Marcus, Jan 22 2025

Status

approved