A329237 The number of base-2 Euler-Jacobi pseudoprimes (A047713) less than 2^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 5, 8, 10, 15, 20, 29, 42, 57, 81, 118, 179, 246, 348, 481, 654, 893, 1231, 1642, 2188, 3003, 4033, 5367, 7252, 9681, 12961, 17460, 23351, 31224, 41623, 55455, 74124, 99127, 132426, 176466, 235792, 314338, 420106, 562476, 751769, 1006184

Offset

1,11

Links

Amiram Eldar, Table of n, a(n) for n = 1..64

Jan Feitsma and William F. Galway, Tables of pseudoprimes and related data.

Example

Below 2^10 = 1024 there is only one Euler-Jacobi pseudoprime, 561. Therefore a(10) = 1.

Mathematica

ejpspQ[n_] := CompositeQ[n] && PowerMod[2, (n - 1)/2, n] == Mod[JacobiSymbol[2, n], n]; s = {}; c = 0; p = 2; n = 1; Do[If[ejpspQ[n], c++]; If[n > p, AppendTo[s, c]; p *= 2], {n, 1, 2^20 + 1, 2}]; s

Crossrefs

Cf. A047713, A055551, A108797, A208276.

Sequence in context: A022799 A314383 A229859 * A314384 A196384 A325176

Adjacent sequences: A329234 A329235 A329236 * A329238 A329239 A329240

Keyword

nonn

Author

Amiram Eldar, Nov 08 2019

Status

approved