

A000445


Latest possible occurrence of the first consecutive pair of nth power residues, modulo any prime.
(Formerly M4652 N1991)


5




OFFSET

2,1


COMMENTS

Don Reble has reported computations proving that 1499876 <= a(8) <= 1508324, which improves on the references below. Note also that it shows a(8) < a(7).  Christopher E. Thompson, Jan 14 2020


REFERENCES

P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory. L'Enseignement Math., Geneva, 1980, p. 87.
W. H. Mills, Bounded consecutive residues and related problems, pp. 170174 of A. L. Whiteman, ed., Theory of Numbers, Proc. Sympos. Pure Math., 8 (1965). Amer. Math. Soc.
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



EXAMPLE

Every large prime has a pair of consecutive quadratic (n=2) residues which appear not later than 9,10, so a(2)=9.  Len Smiley


CROSSREFS



KEYWORD

nonn,nice,more,hard


AUTHOR



EXTENSIONS



STATUS

approved



