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
KEYWORD
nonn,more
AUTHOR
Felix Fröhlich, Jul 18 2016
EXTENSIONS
a(11)-a(16) from Robin Visser, Apr 26 2024
STATUS
approved