A249105
Numbers that form a Pythagorean 5-tuple with their first three arithmetic derivatives.
Original entry on oeis.org
4, 27, 1808, 3125, 12204, 12707, 82377, 269827, 823543, 1412500, 7089739, 9534375, 46873785, 78192979, 372241436
Offset: 1
First three arithmetic derivatives of 1808 are 3632, 7280, 17616 and sqrt(1808^2 + 3632^2 + 7280^2 + 17616^2) = 19488.
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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);
A249107
Numbers that form a Pythagorean 7-tuple with their first five arithmetic derivatives.
Original entry on oeis.org
4031, 10823, 416959, 496939, 1354980, 9146115, 38949392, 44472866, 262908396, 380264131
Offset: 1
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.
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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);
A249110
Numbers that form a Pythagorean 10-tuple with their first eight arithmetic derivatives.
Original entry on oeis.org
4, 27, 3125, 398747, 823543
Offset: 1
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.
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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);
Showing 1-3 of 3 results.
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