OFFSET
0,1
COMMENTS
a(n) is the smallest positive integer m such that m == 7 (mod 8) and for the first n odd primes p, -m is a (nonzero) quadratic residue mod p.
REFERENCES
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).
LINKS
Bert Dobbelaere, Table of n, a(n) for n = 0..50
N. D. Bronson and D. A. Buell, Congruential sieves on FPGA computers, pp. 547-551, in Mathematics of Computation 1943-1993 (Vancouver, 1993), Proc. Symp. Appl. Math., Vol. 48, Amer. Math. Soc. 1994.
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]
PROG
(PARI) {A045535 = (n, m=7)->until(!m+=8, for(i=2, n+1, m%prime(i)||next(2); issquare(Mod(-m, prime(i)))||next(2)); return(m))} \\ Starting value (e.g., a(n-1); must be in 7+8Z) may be given as 2nd arg. - M. F. Hasler, Oct 24 2013
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
The Bronson-Buell reference gives terms through prime(n) = 227.
Edited by Don Reble, Nov 14 2006
Corrected link to OEIS index, following a remark by Don Reble. Values a(0..21) double-checked. - M. F. Hasler, Oct 24 2013
a(27)-a(28) from Jinyuan Wang, Mar 24 2020
More terms from Bert Dobbelaere, Feb 28 2021
STATUS
approved
