|
| |
|
|
A353101
|
|
Least b > 1 such that (b^(prime(n)^2) - 1)/(b^prime(n) - 1) is prime.
|
|
0
|
|
|
|
2, 2, 22, 2, 43, 24, 315, 38, 54, 265, 605, 61, 697, 306, 1153, 370, 2, 10688, 3075, 2338, 1153, 3243, 130, 2301
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The expression is the cyclotomic polynomial value Phi_{p^2}(b) where p=prime(n)=A000040(n).
By definition, a(n) > 1. The occurrences of a(n)=2 correspond exactly to the terms of A156585.
Does a(n) tend to infinity (is liminf a(n) infinite)?
|
|
|
LINKS
|
Table of n, a(n) for n=1..24.
|
|
|
FORMULA
|
a(n) = A085398(prime(n)^2).
|
|
|
PROG
|
(PARI) forprime(p=2, , for(b=2, +oo, if(ispseudoprime(polcyclo(p^2, b)), print1(b, ", "); break())))
(Python)
from sympy import isprime, prime
def a(n, startb=2):
pn = prime(n); pn2 = pn**2; b = startb
while not isprime((b**pn2-1)//(b**pn-1)): b += 1
return b
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Jun 21 2022
|
|
|
CROSSREFS
|
Cf. A000040, A066180, A085398, A156585.
Sequence in context: A082811 A014353 A153438 * A190632 A036110 A143807
Adjacent sequences: A353098 A353099 A353100 * A353102 A353103 A353104
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
Jeppe Stig Nielsen, Apr 24 2022
|
|
|
STATUS
|
approved
|
| |
|
|
