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

Author

N. J. A. Sloane, Apr 06 2014

Keywords

• nonn
• more

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

• 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.

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