A354747 Start with 2*n-1; repeatedly triple and add 2 until reaching a prime. a(n) = number of steps until reaching a prime > 2*n-1, or 0 if no prime is ever reached.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 2, 10, 1, 1, 2, 1, 2, 4, 1, 1, 1, 2, 1, 1, 4, 3, 2, 3, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 2, 1, 3, 3, 1, 1, 2, 3, 3, 5, 1, 1, 1, 2, 3, 9, 1, 1, 2, 1, 2, 4, 1, 2, 1, 6, 1, 1, 2, 1, 1, 5, 1, 3, 1, 2, 1, 1, 3, 1

Offset

1,6

Comments

a(n) is the smallest m >= 1 such that 2*n*3^m - 1 is prime.

The smallest unknown case is n = 100943. Is a(100943) = 0?

If it exists, a(100943) > 30000. - Michael S. Branicky and Jon E. Schoenfield, Jun 07 2022

Links

Table of n, a(n) for n=1..87.

Example

For n = 21: Successively applying the map x -> 3*x+2 to 2*21-1 = 41 yields the sequence 41, 125, 377, 1133, 3401, 10205, 30617, 91853, 275561, 826685, 2480057, reaching the prime 2480057 after 10 steps, so a(21) = 10.

Prog

(PARI) a(n) = my(x=2*n-1, i=0); while(1, x=3*x+2; i++; if(ispseudoprime(x), return(i)))
(Python)
from sympy import isprime
def f(x): return 3*x + 2
def a(n):
    fn, c = f(2*n-1), 1
    while not isprime(fn): fn, c = f(fn), c+1
    return c
print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Jun 06 2022

Crossrefs

Cf. A016789, A050412, A354748.

Sequence in context: A359305 A138330 A128591 * A254444 A102005 A051700

Adjacent sequences: A354744 A354745 A354746 * A354748 A354749 A354750

Keyword

nonn

Author

Felix Fröhlich, Jun 06 2022

Status

approved