A173331 - OEIS

A173331

Second of two intermediate sequences for integral solution of A002144(n)=x^2+y^2.

2, 2, 13, 2, 31, 4, 2, 55, 8, 81, 4, 91, 99, 105, 133, 10, 6, 2, 10, 181, 183, 227, 8, 237, 16, 10, 14, 265, 2, 301, 303, 16, 18, 8, 355, 379, 6, 381, 389, 14, 421, 429, 453, 451, 487, 20, 531, 543, 20, 24, 585, 24, 18, 16, 637, 631, 655, 12, 651, 675, 22, 731, 26, 741, 757

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OFFSET

1,1

COMMENTS

a(n) = A173330(n)*A010050(A005098(n)) mod A002144(n);

A002973(n) = MIN(a(n), A002144(n) - a(n)) / 2.

REFERENCES

H. Davenport, The Higher Arithmetic (Cambridge University Press 7th ed., 1999), ch. V.3, p.122.

LINKS

Table of n, a(n) for n=1..65.

FORMULA

a(n) = ((2k)! / 2(k!))^2 mod p, where p = 4*k+1 = A002144(n).