|
|
A241482
|
|
Least fundamental discriminant D > 1 such that the first n primes p have (D/p) >= 0.
|
|
2
|
|
|
8, 12, 24, 60, 60, 364, 984, 1596, 1596, 1596, 3705, 58444, 84396, 164620, 172236, 369105, 369105, 731676, 731676, 3442296, 3442296, 32169916, 32169916, 47973864, 47973864, 47973864, 313114620, 313114620, 313114620, 313114620, 13461106065, 27765196680, 40527839121, 55213498824, 55213498824, 381031123720
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
By the Chinese Remainder Theorem and Prime Number Theorem in arithmetic progressions, this sequence is infinite.
a(n) is the least fundamental discriminant D > 1 such that the first n primes either decompose or ramify in the real quadratic field with discriminant D. See A306218 for the imaginary quadratic field case. - Jianing Song, Feb 14 2019
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
(364/2) = 0, (364/3) = 1, (364/5) = 1, (364/7) = 0, (364/11) = 1, (364/13) = 0, so 3, 5, 11 decompose in Q[sqrt(91)] and 2, 7, 13 ramify in Q[sqrt(-231)]. For other fundamental discriminants 1 < D < 364, at least one of 2, 3, 5, 7, 11, 13 is inert in the imaginary quadratic field with discriminant D, so a(6) = 364. - Jianing Song, Feb 14 2019
|
|
PROG
|
(PARI) a(n) = my(i=2); while(!isfundamental(i)||sum(j=1, n, kronecker(i, prime(j))==-1)!=0, i++); i \\ Jianing Song, Feb 14 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|