A239902 Exceptional primes: those for which Eq. (4.8) in Cosgrave and Dilcher (2011) fails.

13, 181, 2521, 76543, 489061, 6811741, 1321442641, 18405321661, 381765135195632792959100810331957408101589361

Offset

1,1

Comments

Comments from Christopher M. Stokes, Aug 02 2022: (Start)

Also the primes p for which A047788(p-1) = 0 mod p^2.

Also the primes for which the cyclotomic lambda invariant of Q(sqrt{-3}) is greater than 1. (End)

References

J. B. Cosgrave, A Mersenne-Wieferich Odyssey, Manuscript, May 2022. See Section 18.6.

Links

Table of n, a(n) for n=1..9.

J. B. Cosgrave and K. Dilcher, The multiplicative orders of certain Gauss factorials, Intl. J. Number Theory 7 (1) (2011) 145-171.

John B. Cosgrave and Karl Dilcher, The multiplicative orders of certain Gauss factorials II, Funct. Approx. Comment. Math. Volume 54, Number 1 (2016), 73-93.

D. S. Dummit, D. Ford, H. Kisilevsky, and J. W. Sands, Computation of Iwasawa lambda invariants for imaginary quadratic fields, Journal of number theory, 37(1) (1991), 100-121. [Reference added by N. J. A. Sloane, Jun 24 2022]

Christopher Stokes, On Gauss factorials and their application to Iwasawa theory for imaginary quadratic fields, arXiv:2207.07804 [math.NT], 2022.

Crossrefs

Cf. A354772, A117808.

Sequence in context: A189432 A001570 A122571 * A020544 A009015 A067385

Adjacent sequences: A239899 A239900 A239901 * A239903 A239904 A239905

Keyword

nonn,more

Author

N. J. A. Sloane, Apr 06 2014

Extensions

More terms from Cosgrave (2022), Section 18.6 added by N. J. A. Sloane, May 29 2022

a(9) from Stokes (2022) added by Michel Marcus, Jul 20 2022

Status

approved