A002342 Least positive integer x 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 M3758 N1534)

5, 7, 9, 11, 12, 13, 16, 17, 17, 19, 19, 22, 21, 23, 24, 26, 27, 29, 27, 28, 29, 32, 31, 31, 33, 32, 34, 33, 37, 37, 37, 39, 41, 39, 41, 43, 41, 41, 42, 43, 44, 46, 43, 44, 47, 49, 46, 47, 47, 49, 48, 49, 53, 51, 52, 53, 56, 57, 53, 53, 54, 59, 56, 57, 58, 59, 59, 57, 58, 61

Offset

1,1

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..70.

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)=5;
11 = (7^2 - 5*1^2)/4 so a(2)=7.

Prog

(PARI) a(n)=local(y, p); if(n<1, 0, p=0; y=2; until(p>=n, y++; if(issquare(5+O(prime(y))), p++)); p=prime(y); y=0; until(issquare(4*p+5*y^2), y++); sqrtint(4*p+5*y^2))

Crossrefs

Cf. A002343, A038872.

Sequence in context: A336122 A241853 A165513 * A080353 A184108 A254760

Adjacent sequences: A002339 A002340 A002341 * A002343 A002344 A002345

Keyword

nonn

Author

N. J. A. Sloane

Status

approved