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A307809 Smallest "non-residue" pseudoprime to base prime(n). 2
3277, 3281, 121463, 491209, 11530801, 512330281, 15656266201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..7.

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]

CROSSREFS

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

Sequence in context: A260410 A223430 A307767 * A141629 A116460 A245482

Adjacent sequences:  A307806 A307807 A307808 * A307810 A307811 A307812

KEYWORD

nonn,hard,more

AUTHOR

Amiram Eldar and Thomas Ordowski, Apr 30 2019

EXTENSIONS

a(7) from Daniel Suteu, Apr 30 2019

STATUS

approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)