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

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

Offset: 0

Author

Felix Fröhlich, Jun 20 2022

Keywords

• nonn
• easy

Comments

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)?

Links

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

Crossrefs

Cf. A016789, A052333, A354747, A354748.

Programs

Mathematica

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

Python

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

Formula

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