A190568 Number of squares between powers of 2, floor(sqrt(2^(n+1))) - floor(sqrt(2^n))

1, 0, 1, 0, 2, 1, 3, 3, 5, 6, 10, 13, 19, 26, 38, 53, 75, 106, 150, 212, 300, 424, 600, 848, 1200, 1696, 2400, 3393, 4799, 6786, 9598, 13572, 19196, 27145, 38391, 54291, 76781, 108583, 153561, 217167, 307121, 434334, 614242, 868668, 1228484, 1737337, 2456967, 3474675, 4913933

Offset

-1,5

Comments

A190568(n)/A190568(n-1) converges to sqrt(2) (A002193). - John W. Nicholson, May 15 2011

Links

Charles R Greathouse IV, Table of n, a(n) for n = -1..6646

Formula

a(n) = floor(sqrt(2^(n+1))) - floor(sqrt(2^n)).

Example

Between 2^6=64 and 2^(6+1)=128 are the squares 81=9^2, 100=10^2, 121=11^2, so a(n)=3

Mathematica

Table[Floor[Sqrt[2^(n + 1)]] - Floor[Sqrt[2^n]], {n, -1, 120}] (* G. C. Greubel, Aug 19 2018 *)

Prog

(PARI) a(n)=sqrtint(1<<(n+1))-sqrtint(1<<n) \\ Charles R Greathouse IV, May 12 2011
(Magma) [Floor(Sqrt(2^(n+1))) - Floor(Sqrt(2^n)): n in [-1..50]]; // G. C. Greubel, Aug 19 2018

Crossrefs

Cf. A000079, A000290

Sequence in context: A173510 A238785 A241389 * A340623 A059876 A095354

Adjacent sequences: A190565 A190566 A190567 * A190569 A190570 A190571

Keyword

nonn,easy

Author

John W. Nicholson, May 12 2011

Extensions

Definition corrected by Bruno Berselli, May 13 2011

Status

approved