

A045535


Least negative pseudosquare modulo the first n odd primes.
(Formerly M4381 N2226)


14



7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 118271, 366791, 366791, 2155919, 2155919, 2155919, 6077111, 6077111, 98538359, 120293879, 131486759, 131486759, 508095719, 2570169839, 2570169839, 2570169839, 2570169839, 2570169839, 2570169839
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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.
a(29) > 2*10^10.  Jinyuan Wang, Mar 24 2020


REFERENCES

N. D. Bronson and D. A. Buell, Congruential sieves on FPGA computers, pp. 547551 of Mathematics of Computation 19431993 (Vancouver, 1993), Proc. Symp. Appl. Math., Vol. 48, Amer. Math. Soc. 1994.
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

Table of n, a(n) for n=0..28.
D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433451.
D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433451 [Annotated scanned copy]
OEIS Index entries for sequences related to pseudosquares


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(n1); must be in 7+8Z) may be given as 2nd arg.  M. F. Hasler, Oct 24 2013


CROSSREFS

Cf. A002189, A062241.
Sequence in context: A139852 A141194 A198644 * A001984 A147972 A002223
Adjacent sequences: A045532 A045533 A045534 * A045536 A045537 A045538


KEYWORD

nonn,nice,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

The BronsonBuell reference gives terms through 227. The Math. Comp. version is erroneous.
Edited by Don Reble, Nov 14 2006
Corrected link to OEIS index, following a remark by Don Reble. Values a(0..21) doublechecked.  M. F. Hasler, Oct 24 2013
a(27)a(28) from Jinyuan Wang, Mar 24 2020


STATUS

approved



