A336015 Irregular triangle where row n lists primes q below the n-th primorial such that the multiplicative order of q mod the n-th primorial is 2. I.e., such primes q having the least k such that q^k (mod primorial(n)) == 1 is 2.

5, 11, 19, 29, 29, 41, 71, 139, 181, 419, 461, 659, 769, 881, 1231, 1429, 2309, 1429, 2729, 4159, 5279, 5851, 8009, 8581, 10009, 12011, 12739, 13441, 13859, 14741, 15289, 17291, 20021, 23869, 24179, 30029, 1429, 23869, 77351, 95369, 102101, 116689, 120121, 188189

Offset: 2

Author

Michael De Vlieger, David James Sycamore, David A. Corneth, Jul 08 2020

Keywords

• nonn
• tabf

Examples

			Table begins:
5;
11, 19, 29;
29, 41, 71, 139, 181;
419, 461, 659, 769, 881, 1231, 1429, 2309;
...
For row 2 we look for primes q such that q^2 == 1 (mod primorial(2)) == 1 (mod 6) where q is coprime to 6. It turns out the only prime with this property is 5 as 5^2 == 1 (mod 6). - _David A. Corneth_, Aug 15 2020
		

Links

• David A. Corneth, Table of n, a(n) for n = 2..10001

Crossrefs

Cf. A000010, A002110, A005867, A336016.

Programs

Mathematica

Table[Function[P, Select[Prime@ Range[n, PrimePi[P - 1]], MultiplicativeOrder[#, P] == 2 &]][Product[Prime@ i, {i, n}]], {n, 8}] // Flatten

PARI

row(n) = my(pp = vecprod(primes(n)), res=List()); forstep(i=pp/prime(n)+1, pp-1, 2, if(gcd(i,pp) == 1 && znorder(Mod(i,pp)) == 2 && isprime(i), listput(res,i))); res \\ David A. Corneth, Jul 08 2020

Extensions

New name from David A. Corneth, Aug 15 2020