A307809 Smallest "non-residue" pseudoprime to base prime(n).

3277, 3281, 121463, 491209, 11530801, 512330281, 15656266201

Offset: 1

Author

Amiram Eldar and Thomas Ordowski, Apr 30 2019

Keywords

• nonn
• hard
• more

Comments

a(n) is the smallest odd composite k, with q = A020649(k) = prime(n), such that q^((k-1)/2) == -1 (mod k).

a(8) <= 139309114031, a(9) <= 7947339136801, a(10) <= 72054898434289, a(11) <= 334152420730129, a(12) <= 17676352761153241, a(13) <= 172138573277896681. - Daniel Suteu, Apr 30 2019

Crossrefs

Cf. A000229, A020649, A307767 (the "non-residue" pseudoprimes).

Programs

Mathematica

residueQ[n_, m_] := Module[{ans = 0}, Do[If[Mod[k^2, m] == n, ans = True; Break[]], {k, 0, Floor[m/2]}]; ans]; A020649[n_] := Module[{m = 0}, While[ residueQ[m, n], m++]; m]; a[n_] := Module[{p = Prime[n], k = 3}, While[PrimeQ[k] || PowerMod[p, (k-1)/2, k] != k-1 || A020649[k] != p , k+=2]; k]; Array[a, 6]

Extensions

a(7) from Daniel Suteu, Apr 30 2019