A249107 Numbers that form a Pythagorean 7-tuple with their first five arithmetic derivatives.

4031, 10823, 416959, 496939, 1354980, 9146115, 38949392, 44472866, 262908396, 380264131

Offset

1,1

Comments

If we consider Pythagorean 8-tuple and 9-tuple there are no terms up to n = 10^8.

Links

Table of n, a(n) for n=1..10.

Example

First five arithmetic derivatives of 4031 are 168, 332, 336, 832, 2560 and sqrt(4031^2 + 168^2 + 332^2 + 336^2 + 832^2 + 2560^2) = 4873.

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, 5);

Crossrefs

Cf. A003415, A210503, A230543, A249105, A249106, A249110.

Sequence in context: A258401 A258883 A352752 * A329881 A234838 A234834

Adjacent sequences: A249104 A249105 A249106 * A249108 A249109 A249110

Keyword

nonn,more

Author

Paolo P. Lava, Oct 21 2014

Extensions

a(5)-a(6) from Ray Chandler, Dec 22 2016

a(7)-a(8) from Ray Chandler, Dec 23 2016

a(9) from Ray Chandler, Jan 02 2017

a(10) from Ray Chandler, Jan 08 2017

Status

approved