

A077034


a(1)=3; a(2n), a(2n+1) are smallest integers > a(2n1) such that a(2n1)^2+a(2n)^2=a(2n+1)^2.


1



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
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OFFSET

1,1


COMMENTS

Note that each time two more terms are added simultaneously. The sequence is infinite.
Smallest sequence of Pythagorean triples {a(k1),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 2prime 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 2prime and 3prime Pythagorean triangles are given respectively by A048270 and A048295. The starting term for the smallest nprime Pythagorean triangle is A105318.  Lekraj Beedassy, Sep 16 2005
a(2n) <= (a(2n1)^21)/2; a(2n+1) <= (a(2n1)^2+1)/2. [From Max Alekseyev, May 11 2011]


LINKS

Table of n, a(n) for n=1..31.


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

Cf. A068340, A076542, A077030A077033.
Sequence in context: A055493 A109350 A239356 * A076601 A242669 A090829
Adjacent sequences: A077031 A077032 A077033 * A077035 A077036 A077037


KEYWORD

nonn


AUTHOR

Zak Seidov, Oct 21 2002


EXTENSIONS

More terms from Max Alekseyev, May 11 2011


STATUS

approved



