cp's OEIS Frontend

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.

%I A336015 #32 Dec 06 2020 06:29:04
%S A336015 5,11,19,29,29,41,71,139,181,419,461,659,769,881,1231,1429,2309,1429,
%T A336015 2729,4159,5279,5851,8009,8581,10009,12011,12739,13441,13859,14741,
%U A336015 15289,17291,20021,23869,24179,30029,1429,23869,77351,95369,102101,116689,120121,188189
%N 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.
%H A336015 David A. Corneth, <a href="/A336015/b336015.txt">Table of n, a(n) for n = 2..10001</a>
%e A336015 Table begins:
%e A336015 5;
%e A336015 11, 19, 29;
%e A336015 29, 41, 71, 139, 181;
%e A336015 419, 461, 659, 769, 881, 1231, 1429, 2309;
%e A336015 ...
%e A336015 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
%t A336015 Table[Function[P, Select[Prime@ Range[n, PrimePi[P - 1]], MultiplicativeOrder[#, P] == 2 &]][Product[Prime@ i, {i, n}]], {n, 8}] // Flatten
%o A336015 (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
%Y A336015 Cf. A000010, A002110, A005867, A336016.
%K A336015 nonn,tabf
%O A336015 2,1
%A A336015 _Michael De Vlieger_, _David James Sycamore_, _David A. Corneth_, Jul 08 2020
%E A336015 New name from _David A. Corneth_, Aug 15 2020