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A275118
Split primes p such that prime P lying above p is a Wieferich place of K (with discriminant D_K), for some imaginary quadratic field K of class number 1.
0
5, 11, 13, 181, 1523, 1741, 2521, 19531, 24421, 29789, 76543, 108529, 489061, 880301, 1769069, 6811741
OFFSET
1,1
LINKS
D. S. Dummit, D. Ford, H. Kisilevsky, and J. W. Sands, Computation of Iwasawa Lambda invariants for imaginary quadratic fields, Journal of Number Theory, Vol. 37, No. 1 (1991), 100-121.
Á. Lozano-Robledo, Bernoulli-Hurwitz numbers, Wieferich primes and Galois representations, Journal of Number Theory, Vol. 130, No. 3 (2010), 539-558. See table 2 on page 555.
PROG
(Sage)
def is_A275118(k):
if not Integer(k).is_prime(): return False
for D in [1, 2, 3, 7, 11, 19, 43, 67, 163]:
fct = QuadraticField(-D).ideal(k).factor()
if len(fct)==2:
pi = fct[1][0].gens_reduced()[0]
if (pi^(k-1) - 1).valuation(fct[0][0]) > 1: return True
return False
print([k for k in range(10^7) if is_A275118(k)]) # Robin Visser, Apr 26 2024
CROSSREFS
Cf. A239902.
Sequence in context: A236411 A073615 A346147 * A275640 A275805 A340605
KEYWORD
nonn,more
AUTHOR
Felix Fröhlich, Jul 18 2016
EXTENSIONS
a(11)-a(16) from Robin Visser, Apr 26 2024
STATUS
approved