A375155 a(n) = 2*a(n-1) + 1 for a(n-1) not prime, otherwise a(n) = prime(n) - 1; with a(1) = 147.

147, 295, 591, 1183, 2367, 4735, 9471, 18943, 37887, 75775, 151551, 303103, 606207, 1212415, 2424831, 4849663, 9699327, 19398655, 38797311, 77594623, 155189247, 310378495, 620756991, 1241513983, 2483027967, 4966055935, 9932111871, 19864223743, 39728447487, 79456894975

Offset: 1

Author

Chai Wah Wu, Aug 01 2024

Keywords

• nonn

Comments

Variant of A374965 with initial condition a(1) = 147. If a(1) is prime, the trajectory is: a(1), 2, 4, 9, ... and matches A374965 after the second term. It appears that for most composite a(1), the trajectories also converge towards A374965. This could be due to A050412(n) being small for many composite n.

a(1) = 147 is the first composite number where the trajectory appears not to converge towards A374965.

Other values of a(1) for which the trajectory converges to this sequence are: 295, 591, 1183, 2278, 2367, 3328, 4557, 4602, 4735, 5950, 6072, 6657, 7227, 9115, 9205, 9471, 9612, 9912, 9955, ...

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..7697

Crossrefs

Cf. A050412, A052333, A373799, A374965.

Programs

Mathematica

Module[{n = 1}, NestList[If[n++; PrimeQ[#], Prime[n] - 1, 2*# + 1] &, 147, 50]] (* Paolo Xausa, Aug 02 2024 *)

Python

from itertools import islice
from sympy import isprime, nextprime
def A375155_gen(): # generator of terms
    a, p = 147, 3
    while True:
        yield a
        a, p = p-1 if isprime(a) else (a<<1)|1, nextprime(p)
A375155_list = list(islice(A375155_gen(),40))