A045535 - OEIS

%I M4381 N2226 #35 Feb 28 2021 14:16:26

%S 7,23,71,311,479,1559,5711,10559,18191,31391,118271,366791,366791,

%T 2155919,2155919,2155919,6077111,6077111,98538359,120293879,131486759,

%U 131486759,508095719,2570169839,2570169839,2570169839,2570169839,2570169839,2570169839,328878692999,328878692999,513928659191,844276851239

%N Least negative pseudosquare modulo the first n odd primes.

%C 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.

%D N. D. Bronson and D. A. Buell, Congruential sieves on FPGA computers, pp. 547-551 of Mathematics of Computation 1943-1993 (Vancouver, 1993), Proc. Symp. Appl. Math., Vol. 48, Amer. Math. Soc. 1994.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H Bert Dobbelaere, <a href="/A045535/b045535.txt">Table of n, a(n) for n = 0..50</a>

%H D. H. Lehmer, E. Lehmer and D. Shanks, <a href="https://doi.org/10.1090/S0025-5718-1970-0271006-X">Integer sequences having prescribed quadratic character</a>, Math. Comp., 24 (1970), 433-451.

%H D. H. Lehmer, E. Lehmer and D. Shanks, <a href="/A002189/a002189.pdf">Integer sequences having prescribed quadratic character</a>, Math. Comp., 24 (1970), 433-451 [Annotated scanned copy]

%H <a href="/index/Ps#pseudo-squares">OEIS Index entries for sequences related to pseudo-squares</a>

%o (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

%Y Cf. A002189, A062241.

%K nonn,nice

%O 0,1

%A _N. J. A. Sloane_

%E The Bronson-Buell reference gives terms through 227. The Math. Comp. version is erroneous.

%E Edited by _Don Reble_, Nov 14 2006

%E Corrected link to OEIS index, following a remark by _Don Reble_. Values a(0..21) double-checked. - _M. F. Hasler_, Oct 24 2013

%E a(27)-a(28) from _Jinyuan Wang_, Mar 24 2020

%E More terms from _Bert Dobbelaere_, Feb 28 2021