A230543 Numbers n that form a Pythagorean quadruple with n', n'' and sqrt(n^2 + n'^2 + n''^2), where n' and n'' are the first and the second arithmetic derivative of n.

512, 1203, 3456, 6336, 23328, 42768, 157464, 249753, 288684, 400000, 722718, 1062882, 1948617, 2700000, 4950000, 18225000, 33412500, 105413504, 123018750, 225534375, 312500000, 408918816

Offset

1,1

Comments

Tested up to n = 4.09*10^8.

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Pythagorean Quadruple

Example

If n = 6336 then n' = 23808, n'' = 103936 and sqrt(n^2 + n'^2 + n''^2) = 106816.

Maple

with(numtheory): P:= proc(q) local a1, a2, n, p;
for n from 2 to q do a1:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
a2:=a1*add(op(2, p)/op(1, p), p=ifactors(a1)[2]);
if type(sqrt(n^2+a1^2+a2^2), integer) then print(n);
fi; od; end: P(10^10);

Crossrefs

Cf. A003415, A009003, A009004, A068346, A210503, A211176.

Cf. A096907-A096909 and A097263-A097266 for Pythagorean Quadruples.

Sequence in context: A220017 A234879 A202454 * A224651 A224644 A258726

Adjacent sequences: A230540 A230541 A230542 * A230544 A230545 A230546

Keyword

nonn,more

Author

Paolo P. Lava, Oct 25 2013

Extensions

a(16)-a(18) from Giovanni Resta, Oct 25 2013

a(19) from Ray Chandler, Dec 22 2016

a(20) from Ray Chandler, Dec 31 2016

a(21) from Ray Chandler, Jan 05 2017

a(22) from Ray Chandler, Jan 09 2017

Status

approved