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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.
7

%I #10 Mar 06 2021 10:41:40

%S 1,1,4,2,64,59,1342,1076,4268,10739,64387,818998,3226976,26444853,

%T 53155423,1175849126,13396689992,2368807981,907313696551,483703442648,

%U 2835669288809,98713800566163

%N 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.

%e 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.

%o (PARI) prd(n) = my(q=3, t=1); for(k=1, n, until(q%4==1, q=nextprime(q+1)); t*=q); t; \\ A006278

%o a(n) = {my(t=prd(n), q=0); until(issquare(t-q^2), q++); q; } \\ _Michel Marcus_, Mar 05 2021

%Y Cf. A002144, A006278, A236382.

%K nonn,more

%O 1,3

%A _Colin Barker_, Jan 24 2014