A245206 Odd primes p with E_{p-3}(1/4) == 0 (mod p), where E_n(x) denotes the Euler polynomial of degree n.

1019

Offset

1,1

Comments

The conjecture in A245204 asserts that the current sequence contains infinitely many primes.

Our computation shows that the second term should be greater than prime(2600) = 23321.

Links

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

Zhi-Wei Sun, Super congruences and Euler numbers, arXiv:1001.4453 [math.NT].

Zhi-Wei Sun, Super congruences and Euler numbers, Sci. China Math. 54(2011), 2509-2535.

Index entries for one-term sequences

Example

a(1) = 1019 since 1019 is a prime with E_{1019-3}(1/4) == 88*1019 (mod 1019^2).

Mathematica

rMod[m_, n_]:=Mod[Numerator[m]*PowerMod[Denominator[m], -1, n], n, -n/2]
n=0; Do[If[rMod[EulerE[Prime[k]-3, 1/4], Prime[k]]==0, n=n+1; Print[n, " ", Prime[k]]], {k, 2, 200}]

Crossrefs

Cf. A000040, A122045, A001586, A198245, A245089, A245204.

Sequence in context: A235811 A051982 A210139 * A340872 A104444 A157510

Adjacent sequences: A245203 A245204 A245205 * A245207 A245208 A245209

Keyword

nonn,more

Author

Zhi-Wei Sun, Jul 13 2014

Status

approved