A249105 Numbers that form a Pythagorean 5-tuple with their first three arithmetic derivatives.

4, 27, 1808, 3125, 12204, 12707, 82377, 269827, 823543, 1412500, 7089739, 9534375, 46873785, 78192979, 372241436

Offset: 1

Author

Paolo P. Lava, Oct 21 2014

Keywords

• nonn
• more

Examples

			First three arithmetic derivatives of 1808 are 3632, 7280, 17616 and sqrt(1808^2 + 3632^2 + 7280^2 + 17616^2) = 19488.
		

Crossrefs

A051674 is a subsequence.

Cf. A003415, A210503, A230543, A249106, A249107, A249110.

Programs

Maple

with(numtheory);
Dr:=proc(w) local x,p; x:=w*add(op(2,p)/op(1,p),p=ifactors(w)[2]); end:
P:=proc(q,h) local a,b,k,n; for n from 2 to q do a:=n; b:=n^2;
for k from 1 to h do a:=Dr(a); b:=b+a^2; od; if type(sqrt(b),integer) then print(n);
fi; od; end: P(10^9,3);

Extensions

a(13) from Ray Chandler, Dec 23 2016

a(14) from Ray Chandler, Dec 24 2016

a(15) from Ray Chandler, Jan 08 2017