A249110 Numbers that form a Pythagorean 10-tuple with their first eight arithmetic derivatives.

4, 27, 3125, 398747, 823543

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Example

First eight arithmetic derivatives of 398747 are 1692, 2856, 5812, 5816, 8732, 9116, 9500, 15700 and sqrt(398747^2 + 1692^2 + 2856^2 + 5812^2 + 5816^2 + 8732^2 + 9116^2 + 9500^2 + 15700^2) = 399467.

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, 8);

Crossrefs

A051674 is a subsequence. - Ray Chandler, Dec 22 2016

Cf. A003415, A051674, A210503, A230543, A249105, A249106, A249107.

Sequence in context: A066352 A357561 A249105 * A348329 A051674 A132641

Adjacent sequences: A249107 A249108 A249109 * A249111 A249112 A249113

Keyword

nonn,more

Author

Paolo P. Lava, Oct 21 2014

Status

approved