A236381 Smallest value of x such that x^2 + y^2 = P, where P is the product of the first n primes of the form 4k + 1, and 0 < x < y.

1, 1, 4, 2, 64, 59, 1342, 1076, 4268, 10739, 64387, 818998, 3226976, 26444853, 53155423, 1175849126, 13396689992, 2368807981, 907313696551, 483703442648, 2835669288809, 98713800566163, 24423236756993, 6054940274199961, 17628259859562384, 128658404383205917, 3865377837569367511

Offset: 1

Author

Colin Barker, Jan 24 2014

Keywords

• nonn

Examples

			a(3) = 4 because the solutions to x^2 + y^2 = 5*13*17 are (x,y) = (23,24), (9,32), (4,33), (12,31) of which the smallest value of x is 4.
		

Crossrefs

Cf. A002144, A006278, A236382, A341678.

Programs

PARI

prd(n) = my(q=3, t=1); for(k=1, n, until(q%4==1, q=nextprime(q+1)); t*=q); t; \\ A006278
a(n) = {my(t=prd(n), q=0); until(issquare(t-q^2), q++); q; } \\ Michel Marcus, Mar 05 2021

Extensions

a(23)-a(27) from Jinyuan Wang, Apr 30 2025