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

1,1

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: A110763 A066352 A357561 * A249110 A348329 A051674

Adjacent sequences: A249102 A249103 A249104 * A249106 A249107 A249108

Keyword

nonn,more

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