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A249107 Numbers that form a Pythagorean 7-tuple with their first five arithmetic derivatives. 3
4031, 10823, 416959, 496939, 1354980, 9146115, 38949392, 44472866, 262908396, 380264131 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If we consider Pythagorean 8-tuple and 9-tuple there are no terms up to n = 10^8.
LINKS
EXAMPLE
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.
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, 5);
CROSSREFS
Sequence in context: A258401 A258883 A352752 * A329881 A234838 A234834
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Oct 21 2014
EXTENSIONS
a(5)-a(6) from Ray Chandler, Dec 22 2016
a(7)-a(8) from Ray Chandler, Dec 23 2016
a(9) from Ray Chandler, Jan 02 2017
a(10) from Ray Chandler, Jan 08 2017
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)