A001988 -id:A001988 - cp's OEIS frontend

A001989 Class numbers associated with terms of A001988.

1, 1, 5, 7, 7, 7, 9, 53, 73, 83, 83, 83, 157, 185, 185, 185, 185, 1927, 2295, 2273, 5313, 5313, 7173, 9529, 18545, 18545, 18545, 18545, 22635, 22635, 66011, 121725, 344909, 344909

Offset: 1

N. J. A. Sloane

nonn

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. A001988.

isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(p, q) != -kronecker(-1, q), return (0)); ); return (1); }
a(n) = {my(oddpn = prime(n+1)); forprime(p=3, , if (((p%8) == 7) &&  isok(p, oddpn), return (qfbclassno(-p*if(p%4>1, 4, 1)))););} \\ Michel Marcus, Oct 19 2017

Better name from Sean A. Irvine, Mar 06 2013
Terms corrected by Sean A. Irvine, Mar 06 2013
Offset changed by Michel Marcus, Oct 19 2017

A001990 Let p be the n-th odd prime. a(n) is the least prime congruent to 5 modulo 8 such that Legendre(-a(n), q) = -Legendre(-2, q) for all odd primes q <= p.

Original entry on oeis.org

5, 29, 29, 29, 29, 29, 29, 29, 23669, 23669, 23669, 23669, 23669, 23669, 1508789, 5025869, 9636461, 9636461, 9636461, 37989701, 37989701, 37989701, 37989701, 37989701, 240511301, 240511301

Offset: 1

N. J. A. Sloane

nonn

Numbers so far are all congruent to 5 (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. A001988.

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, if (isok(p, oddpn), return (p));););} \\ Michel Marcus, Oct 18 2017

Better name from Sean A. Irvine, Mar 06 2013

Name and offset corrected by Michel Marcus, Oct 18 2017

cp's OEIS Frontend

A001989 Class numbers associated with terms of A001988.

Views

Author

Keywords

References

Links

Crossrefs

Programs

PARI

Extensions