

A249105


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


3



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

1,1


LINKS

Table of n, a(n) for n=1..15.


EXAMPLE

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


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);


CROSSREFS

A051674 is a subsequence.
Cf. A003415, A210503, A230543, A249106, A249107, A249110.
Sequence in context: A271385 A110763 A066352 * A249110 A051674 A132641
Adjacent sequences: A249102 A249103 A249104 * A249106 A249107 A249108


KEYWORD

nonn


AUTHOR

Paolo P. Lava, Oct 21 2014


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


STATUS

approved



