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, 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

Table of n, a(n) for n=1..97.

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.

Cf. A002342, A038872.

Sequence in context: A245049 A214261 A097825 * A082076 A231516 A048793

Adjacent sequences: A002340 A002341 A002342 * A002344 A002345 A002346

Keyword

nonn

Author

N. J. A. Sloane

Status

approved