A077034 a(1)=3; a(2n), a(2n+1) are smallest integers > a(2n-1) such that a(2n-1)^2+a(2n)^2=a(2n+1)^2.

3, 4, 5, 12, 13, 84, 85, 132, 157, 12324, 12325, 15960, 20165, 26280, 33125, 79500, 86125, 95400, 128525, 152040, 199085, 477804, 517621, 871500, 1013629, 513721874820, 513721874821, 4351526469072, 4381745402885, 10516188966924, 11392538047501

Offset: 1

Author

Zak Seidov, Oct 21 2002

Keywords

• nonn

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]

Examples

			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

Cf. A048270, A048295, A076604, A105318.

Extensions

More terms from Max Alekseyev, May 11 2011