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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

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Last modified August 10 03:07 EDT 2022. Contains 356029 sequences. (Running on oeis4.)