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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A000010, A002110, A005867, A336016.

Sequence in context: A333675 A051349 A048217 * A132087 A089270 A275068

Adjacent sequences:  A336012 A336013 A336014 * A336016 A336017 A336018

KEYWORD

nonn,tabf

AUTHOR

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

EXTENSIONS

New name from David A. Corneth, Aug 15 2020

STATUS

approved

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Last modified May 12 06:30 EDT 2021. Contains 343814 sequences. (Running on oeis4.)