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A249110 Numbers that form a Pythagorean 10-tuple with their first eight arithmetic derivatives. 3
4, 27, 3125, 398747, 823543 (list; graph; refs; listen; history; text; internal format)
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: A110763 A066352 A249105 * A051674 A132641 A008973

Adjacent sequences:  A249107 A249108 A249109 * A249111 A249112 A249113

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Oct 21 2014

STATUS

approved

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Last modified March 8 13:59 EST 2021. Contains 341949 sequences. (Running on oeis4.)