A231579 a(1) = 7; for n > 1, a(n) is the hypotenuse of the right triangle with legs a(n) - 1 and a(n-1).

7, 25, 313, 48985, 1199765113, 719718163185951385, 258997117209879873736794713791709113, 33539753361514126736178628392779244498735703225085922505721228803623385

Offset: 1

Author

Zak Seidov, Nov 11 2013

Keywords

• nonn

Comments

Least prime factors of a(n): 7, 5, 313, 5, 1199765113, 5, 233, 5, 101, 5, 2951438416261, 5, 457, 5, 373, 5, 89, 5, 101, 5.

Examples

			25^2 = 24^2 + 7^2, 313^2 = 312^2 + 25^2.
		

Crossrefs

Cf. A053630 (case a(1) = 3).

Programs

Mathematica

NestList[(#^2+1)/2&,7,8]

Formula

a(n) = (a(n-1)^2 + 1) / 2.

Extensions

b(11) = 2951438416261 (the least prime factor of a(11)) from Jon E. Schoenfield and Charles R Greathouse IV