A052333 -id:A052333 - cp's OEIS frontend

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

Chai Wah Wu, Aug 01 2024

nonn

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, ...

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

Cf. A050412, A052333, A373799, A374965.

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

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))

A355142 a(n) = 33648*3^n - 1.

Original entry on oeis.org

33647, 100943, 302831, 908495, 2725487, 8176463, 24529391, 73588175, 220764527, 662293583, 1986880751, 5960642255, 17881926767, 53645780303, 160937340911, 482812022735, 1448436068207, 4345308204623, 13035924613871, 39107773841615, 117323321524847, 351969964574543

Offset: 0

Felix Fröhlich, Jun 20 2022

For n > 0, this is the trajectory of 100943 under the map x -> 3*x+2.
100943 is the least starting value > 0 where the trajectory under the map in the previous comment does not reach a prime after a small number of steps.
Are there any primes > 100943 in the sequence (cf. A354747 and A354748)?

Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A016789, A052333, A354747, A354748.

33648*3^Range[0,30]-1 (* or *) LinearRecurrence[{4,-3},{33647,100943},30] (* Harvey P. Dale, Mar 03 2023 *)

PARI
```
a(n) = 33648*3^n-1
```

a = [33647]; [a.append(3*a[-1]+2) for n in range(21)]
print(a) # Michael S. Branicky, Jun 20 2022

G.f.: (33647 - 33645*x)/((1 - x)*(1 - 3*x)). - Stefano Spezia, Jun 21 2022

cp's OEIS Frontend

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

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