A001990 -id:A001990 - cp's OEIS frontend

A001991 Class numbers associated with terms of A001990.

2, 2, 2, 2, 2, 2, 2, 2, 46, 46, 46, 46, 46, 46, 406, 718, 950, 950, 950, 1698, 1698, 1698, 1698, 1698, 3990, 3990, 3990, 53510, 77970, 89478, 89478, 89478, 89478, 89478, 89478

Offset: 1

N. J. A. Sloane

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451.
D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451 [Annotated scanned copy]
Index entries for sequences related to quadratic fields

Cf. A001990.

isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(p, q) != -kronecker(-2, q), return (0)); ); return (1); }
a(n) = {oddpn = prime(n+1); forprime(p=3, , if (((p%8) == 5) && isok(p, oddpn), return (qfbclassno(-8*p))); ); } \\ Michel Marcus, Oct 19 2017

a(n) = ClassNumber(-8*A001990(n)). - Sean A. Irvine, Mar 06 2013

Better name from Sean A. Irvine, Mar 06 2013

Offset changed by Michel Marcus, Oct 19 2017

A001988 Let p be the n-th odd prime. a(n) is the least prime congruent to 7 modulo 8 such that Legendre(-a(n), q) = -Legendre(-1, q) for all odd primes q <= p.

Original entry on oeis.org

7, 7, 127, 463, 463, 487, 1423, 33247, 73327, 118903, 118903, 118903, 454183, 773767, 773767, 773767, 773767, 86976583, 125325127, 132690343, 788667223, 788667223, 1280222287, 2430076903, 10703135983, 10703135983, 10703135983

Offset: 1

N. J. A. Sloane

nonn

Numbers so far are all congruent to 7 (mod 24). - Ralf Stephan, Jul 07 2003

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451.
D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451 [Annotated scanned copy]

Cf. A001990.

isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(p, q) != -kronecker(-1, q), return (0));); return (1);}
a(n) = {oddpn = prime(n+1); forprime(p=3, , if ((p%8) == 7, if (isok(p, oddpn), return (p));););} \\ Michel Marcus, Oct 18 2017

from sympy import legendre_symbol as L, primerange, prime, nextprime
def isok(p, oddpn):
    for q in primerange(3, oddpn + 1):
        if L(p, q)!=-L(-1, q): return 0
    return 1
def a(n):
    oddpn=prime(n + 1)
    p=3
    while True:
        if p%8==7:
            if isok(p, oddpn): return p
        p=nextprime(p) # Indranil Ghosh, Oct 23 2017, after PARI code by Michel Marcus

Better name and more terms from Sean A. Irvine, Mar 06 2013

Name and offset corrected by Michel Marcus, Oct 18 2017

cp's OEIS Frontend

A001991 Class numbers associated with terms of A001990.

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