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Number of primitive Pythagorean quadruples (a, b, c, d) with d < 10^n.
3

%I #23 Mar 01 2023 01:49:08

%S 4,347,34163,3412143,341175325,34117055318,3411700692939,

%T 341170025540426,34117002022924247

%N Number of primitive Pythagorean quadruples (a, b, c, d) with d < 10^n.

%C a(n) ~ (1+G)*A225206(n)/Pi, where G is Catalan's constant (A006752).

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_quadruple">Pythagorean quadruple</a>

%e a(1) = 4 because there are four primitive solutions (a, b, c, d) as follows: (1, 2, 2, 3), (2, 3, 6, 7), (1, 4, 8, 9), (4, 4, 7, 9) with d < 10.

%Y Cf. A096907-A096910, A225206.

%K more,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, May 01 2013

%E a(4) from _Giovanni Resta_, May 01 2013

%E a(5)-a(9) from _Max Alekseyev_, Feb 28 2023