A125652 Numbers m such that m^2=A125650(k) for some k (belonging A125651).

1, 3, 9, 105, 306, 3567, 10395, 121173, 353124, 4116315, 11995821, 139833537, 407504790, 4750223943, 13843167039, 161367780525, 470260174536, 5481754313907, 15975002767185, 186218278892313, 542679833909754

Offset: 1

Author

Alexander Adamchuk, Nov 29 2006, corrected Dec 14 2006

Keywords

• nonn

Comments

Indices k such that a(n)^2=A125650(k) are listed in A125651.

3 divides a(n) for n>1. For n>1 a(n) = 3*A041053(2n-3), where A041053(n) = {1, 1, 2, 3, 32, 35, 67, 102, 1087, 1189, 2276, 3465, ...} Denominators of continued fraction convergents to sqrt(32). - Alexander Adamchuk, Jan 19 2007

Examples

			a(2)=3 because A125650(3)=9=3^2; a(3)=9 because A125650(24)=81=9^2.
		

Crossrefs

Cf. A125650, A125651, A106328.

Cf. A041053.

Formula

a(2k)=A106328(2k); for k>0, a(2k+1)=A106328(2k+1)/2.

a(n) = sqrt(A125650(A125651(n))).

a(n) = 3*A041053(2n-3) for n>1. - Alexander Adamchuk, Jan 19 2007

Extensions

Edited by Max Alekseyev, Jan 11 2007