A017911 Powers of sqrt(2) rounded to nearest integer.

1, 1, 2, 3, 4, 6, 8, 11, 16, 23, 32, 45, 64, 91, 128, 181, 256, 362, 512, 724, 1024, 1448, 2048, 2896, 4096, 5793, 8192, 11585, 16384, 23170, 32768, 46341, 65536, 92682, 131072, 185364, 262144, 370728, 524288

Offset

0,3

Comments

Apart from offset the same as A057048. - T. D. Noe, Apr 27 2003

Indeed, write the natural numbers as triangle, [1; 2, 3; 4, 5, 6; ...], then the last number in each row is T(n) = n(n+1)/2 = A000217(n), and 2^k is located in the row n with n(n-1)/2 < 2^k <= n(n+1)/2 <=> n^2 - n < 2^(k+1) <= n^2 + n, which means that n = round(sqrt(2^(k+1))). - M. F. Hasler, Feb 20 2012

The rounded curvature of circle in square inscribing or the rounded radius of circle in square circumscribing with initial circle radius = 1 for both cases, see illustration in link. - Kival Ngaokrajang, Aug 07 2013

Even-indexed terms are powers of 2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Kival Ngaokrajang, Illustration of initial terms of square inscribing

Eric Weisstein's World of Mathematics, Polygon Inscribing

Example

sqrt(2)^3 = 2.82842712474619..., so a(3) = 3.
sqrt(2)^4 = 4, so a(4) = 4.
sqrt(2)^5 = 5.6568542494923801952..., so a(5) = 6.
sqrt(2)^6 = 8, so a(6) = 8.
sqrt(2)^7 = 11.31370849898476..., so a(7) = 11.

Mathematica

Floor[(Sqrt[2]^Range[0, 40] + 1/2)] (* Vincenzo Librandi, Nov 19 2011 *)

Prog

(PARI) a(n)=round(sqrt(2)^n) \\ Charles R Greathouse IV, Nov 18 2011
(Magma) [Round(Sqrt(2)^n): n in [0..40]]; // Vincenzo Librandi, Nov 19 2011

Crossrefs

Cf. A000079, A057048.

Apart from offset, first differences of A001521.

Sequence in context: A294922 A317669 A208887 * A057048 A281094 A054782

Adjacent sequences: A017908 A017909 A017910 * A017912 A017913 A017914

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved