A175627 a(1) = 1; a(n) is the smallest square > 2*a(n-1).

1, 4, 9, 25, 64, 144, 289, 625, 1296, 2601, 5329, 10816, 21904, 44100, 88209, 177241, 355216, 710649, 1423249, 2849344, 5702544, 11410884, 22829284, 45670564, 91355364, 182736324, 365497924, 730999369, 1462068169, 2924213776, 5848578576, 11697287716, 23394620209, 46789583481

Offset: 1

Author

Ctibor O. Zizka, Dec 04 2010

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055496.

Programs

Mathematica

NestList[(Floor[Sqrt[2#]]+1)^2&,1,40] (* Harvey P. Dale, Jul 26 2017 *)

PARI

{a=1; print1(a, ", "); for(i=1, 40, a=(ceil(sqrt(2*a)))^2; print1(a, ", "))} /* Zak Seidov, Dec 04 2010 */

Formula

a(n) = (ceiling(sqrt(2*a(n-1))))^2.

lim_{n->oo} (a(n+1)/a(n)) = 2.