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A002343
Least positive integer y such that p = (x^2 - 5*y^2)/4 where p is the n-th odd prime such that 5 is a square mod p.
(Formerly M0109 N0042)
1
1, 1, 1, 1, 2, 1, 2, 3, 1, 3, 1, 4, 1, 1, 2, 4, 5, 5, 1, 2, 3, 6, 3, 1, 5, 2, 4, 1, 7, 5, 3, 5, 7, 1, 5, 7, 3, 1, 4, 5, 6, 8, 1, 2, 7, 9, 4, 5, 3, 5, 2, 1, 9, 5, 6, 7, 10, 11, 3, 1, 4, 11, 6, 7, 8, 9, 7, 1, 4, 9, 5, 3, 8, 13, 3, 1, 4, 11, 1, 8, 2, 9, 10, 11, 13, 14, 7, 4, 5, 11, 7, 2, 10, 11, 15, 5, 9
OFFSET
1,5
COMMENTS
The n-th odd prime for which 5 is a square mod p is A038872(n).
REFERENCES
A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
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
A. J. C. Cunningham, Quadratic Partitions, Hodgson, London, 1904. [Annotated scans of selected pages]
EXAMPLE
5 = (5^2 - 5*1^2)/4 so a(1)=1;
11 = (7^2 - 5*1^2)/4 so a(2)=1.
PROG
(PARI) a(n)=local(y, p); if(n<1, 0, p=0; y=1; until(p>=n, y++; if(issquare(5+O(prime(y))), p++)); p=prime(y); y=0; until(issquare(4*p+5*y^2), y++); y)
CROSSREFS
Cf. A002342.
Sequence in context: A245049 A214261 A097825 * A371097 A082076 A231516
KEYWORD
nonn
STATUS
approved