

A198245


Euler primes: Primes p that divide E(p  3), where E(k) is the kth Euler number.


6




OFFSET

1,1


COMMENTS

The evenindexed Euler numbers are A028296, the oddindexed Euler numbers are all zero.
Numerous combinatorial congruences recently obtained by Z. W. Sun and by Z. H. Sun contain the Euler numbers E(p3) with a prime p.
Only three primes less than 3 * 10^6 satisfy this condition (the current members of the sequence).
Such primes have been recently suggested by Z. W. Sun; namely, Sun found the first and the second such primes, 149 and 241, and used them to discover new congruences involving E(p  3).
This is reported by Zhi Wei Sun on Feb 08 2010 and the third prime was found by Romeo Mestrovic (on Sep 26 2011).
Mestrovic (2012) computes that only three primes < 10^7 are in the sequence, but he conjectures that the sequence is infinite.  Jonathan Sondow, Dec 18 2012
Hathi et al. give a(3) as 2124679 and claim that the terms 2124679, 16467631, 17613227 were reported in Cosgrave, Dilcher, 2013, but 2124679 does not appear in table 2 in that paper. How is 2124679 related to this sequence? Note that 2124679 is the second Wolstenholme prime (A088164).  Felix Fröhlich, Apr 27 2021


REFERENCES

J. B. Cosgrave, A MersenneWieferich Odyssey, Manuscript, May 2022. See Section 18.8.


LINKS



MATHEMATICA

Select[Prime[Range[2, 200]], IntegerQ[EulerE[#  3]/#] &] (* Alonso del Arte, Oct 31 2011 *)


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



