A242441 Numbers n such that there are no integer k < sqrt(n) and prime p < n with k^2*p == 1 (mod n).

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 21, 24, 28, 30, 32, 39, 40, 48, 50, 56, 60, 63, 70, 72, 80, 88, 102, 110, 112, 120, 126, 156, 168, 204, 213, 220, 232, 240, 252, 272, 273, 280, 312, 372, 378, 408, 520, 527, 546, 760, 765, 780, 813, 840, 968, 1320, 1715, 1848

Offset

1,2

Comments

Conjecture: The sequence only has 61 terms as listed.

We have checked this extension of the conjecture in A242425 for n up to 10^7.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..61

Example

a(5) = 5 since none of 1^2*2 = 2, 1^2*3 = 3, 2^2*2 = 8 and 2^2*3 = 12 is congruent to 1 modulo 5.

Mathematica

r[k_, n_]:=r[k, n]=PowerMod[k^2, -1, n]
m=0; Do[Do[If[GCD[k, n]==1&&PrimeQ[r[k, n]], Goto[aa]], {k, 1, Sqrt[n-1]}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 2000}]

Crossrefs

Cf. A000040, A000290, A242425, A242444.

Sequence in context: A295298 A003401 A281624 * A064481 A336505 A303704

Adjacent sequences: A242438 A242439 A242440 * A242442 A242443 A242444

Keyword

nonn

Author

Zhi-Wei Sun, May 14 2014

Status

approved