OFFSET
1,1
COMMENTS
Note that each time two more terms are added simultaneously. The sequence is infinite.
Smallest sequence of Pythagorean triples {a(k-1),a(k),a(k+1)},with k=2n,such that the hypotenuse of one triangle is the short leg of the next one. Such a sequence is called 2-prime Pythagorean because only the first two triangles (3,4,5),(5,12,13) both have prime hypotenuse and short leg. The next such sequence is given by A076604. Actually, the starting terms for all 2-prime and 3-prime Pythagorean triangles are given respectively by A048270 and A048295. The starting term for the smallest n-prime Pythagorean triangle is A105318. - Lekraj Beedassy, Sep 16 2005
a(2n) <= (a(2n-1)^2-1)/2; a(2n+1) <= (a(2n-1)^2+1)/2. [Max Alekseyev, May 11 2011]
EXAMPLE
a(1)=3 implies a(2)=4 and a(3)=5: 3^2+4^2=5^2.
a(3)=5 implies a(4)=12 and a(5)=13: 5^2+12^2=13^2.
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 21 2002
EXTENSIONS
More terms from Max Alekseyev, May 11 2011
STATUS
approved