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A249107
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Numbers that form a Pythagorean 7-tuple with their first five arithmetic derivatives.
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3
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OFFSET
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1,1
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COMMENTS
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If we consider Pythagorean 8-tuple and 9-tuple there are no terms up to n = 10^8.
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LINKS
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EXAMPLE
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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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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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