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

%I A249105 #29 Feb 18 2021 00:19:09
%S A249105 4,27,1808,3125,12204,12707,82377,269827,823543,1412500,7089739,
%T A249105 9534375,46873785,78192979,372241436
%N A249105 Numbers that form a Pythagorean 5-tuple with their first three arithmetic derivatives.
%e A249105 First three arithmetic derivatives of 1808 are 3632, 7280, 17616 and sqrt(1808^2 + 3632^2 + 7280^2 + 17616^2) = 19488.
%p A249105 with(numtheory);
%p A249105 Dr:=proc(w) local x,p; x:=w*add(op(2,p)/op(1,p),p=ifactors(w)[2]); end:
%p A249105 P:=proc(q,h) local a,b,k,n; for n from 2 to q do a:=n; b:=n^2;
%p A249105 for k from 1 to h do a:=Dr(a); b:=b+a^2; od; if type(sqrt(b),integer) then print(n);
%p A249105 fi; od; end: P(10^9,3);
%Y A249105 A051674 is a subsequence.
%Y A249105 Cf. A003415, A210503, A230543, A249106, A249107, A249110.
%K A249105 nonn,more
%O A249105 1,1
%A A249105 _Paolo P. Lava_, Oct 21 2014
%E A249105 a(13) from _Ray Chandler_, Dec 23 2016
%E A249105 a(14) from _Ray Chandler_, Dec 24 2016
%E A249105 a(15) from _Ray Chandler_, Jan 08 2017