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A342583
Numbers k such that prime(k) is the hypotenuse of a Pythagorean triple where one leg is also prime.
1
3, 6, 18, 42, 82, 271, 284, 369, 445, 682, 1069, 1193, 1900, 2241, 3894, 6137, 7108, 8164, 9658, 10126, 12645, 14842, 14936, 17913, 18420, 19480, 23893, 24605, 28959, 32913, 36279, 40847, 43936, 44559, 45500
OFFSET
1,1
COMMENTS
In such a triangle, the leg that is not prime is always the largest one and is equal to prime(k)-1; these even legs are in A067755. E.g. for a(2) = 6, prime(6) = 13 and the corresponding Pythagorean triple is (5, 12, 13). - Bernard Schott, Apr 03 2021
LINKS
EXAMPLE
a(1) = 3, since prime(3) = 5 is the hypotenuse of the triple (3,4,5).
MAPLE
R:= NULL: count:= 0:
p:= 2:
while count < 100 do
p:= nextprime(p); n:= (p-1)/2; q:= 2*n^2+2*n+1;
if isprime(q) then
count:= count+1; r:= numtheory:-pi(q); R:= R, r;
fi
od:
R; # Robert Israel, Mar 22 2021
MATHEMATICA
PrimePi[Take[Cases[Import["https://oeis.org/A067756/b067756.txt", "Table"], {_, _}][[All, 2]], 100]]
CROSSREFS
Cf. A067756 (the hypotenuses).
Sequence in context: A356766 A181037 A222856 * A007990 A197050 A354387
KEYWORD
nonn
AUTHOR
Ivan N. Ianakiev, Mar 16 2021
STATUS
approved