A134886 -id:A134886 - cp's OEIS frontend

A175268 a(n)=floor(2^sqrt(n)).

1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 11, 12, 13, 14, 16, 17, 18, 20, 22, 23, 25, 27, 29, 32, 34, 36, 39, 41, 44, 47, 50, 53, 56, 60, 64, 67, 71, 75, 80, 84, 89, 94, 99, 104, 110, 115, 121, 128, 134, 141, 148, 155, 162, 170, 178, 187, 196, 205, 214, 224, 234, 245, 256, 267

Offset: 0

Zak Seidov, Mar 18 2010

nonn

			a(0)=floor(2^sqrt(0))=floor(2^0)=1,
a(1)=floor(2^sqrt(1))=floor(2)=2,
a(2)=floor(2^sqrt(2))=floor(2.665)=2.

Cf. A134886 a(n)=floor(n^sqrt(2)).

Floor[2^Sqrt[Range[0,70]]] (* Harvey P. Dale, Aug 03 2016 *)

A175269 a(n) = floor(2^sqrt(n)) - floor(n^sqrt(2)).

Original entry on oeis.org

1, 1, 0, -1, -3, -5, -7, -9, -11, -14, -17, -20, -22, -25, -28, -32, -34, -37, -41, -44, -47, -51, -54, -57, -60, -62, -66, -69, -72, -75, -78, -81, -84, -87, -90, -92, -94, -98, -100, -102, -104, -106, -108, -110, -111, -113, -114, -116, -117, -117, -118

Offset: 0

Zak Seidov, Mar 18 2010

sign

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A134886, A175268.

[Floor(2^Sqrt(n)) - Floor(n^Sqrt(2)): n in [0..100]]; // G. C. Greubel, Oct 02 2018

Table[Floor[2^Sqrt[n]] - Floor[n^Sqrt[2]], {n, 0, 100}]

vector(100, n, n--; floor(2^sqrt(n)) - floor(n^sqrt(2))) \\ G. C. Greubel, Oct 02 2018

A180448 Primes of the form floor(k^sqrt(2)).

Original entry on oeis.org

2, 7, 29, 37, 41, 59, 79, 89, 197, 281, 311, 431, 491, 571, 607, 617, 673, 683, 751, 997, 1019, 1051, 1117, 1217, 1229, 1297, 1321, 1367, 1571, 1583, 1607, 1657, 1669, 1871, 1949, 2309, 2447, 2503, 2531, 2687, 2903, 3413, 3613, 3739, 3881, 3929, 4057, 4073, 4219

Offset: 1

William A. Tedeschi, Sep 07 2010

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Select[Floor[Range[0,500]^Sqrt[2]],PrimeQ] (* Harvey P. Dale, May 20 2011 *)

for(n=1, 154392, if(ispseudoprime(t=floor(n^sqrt(2))), print1(t", "))); v \\ Charles R Greathouse IV, Feb 18 2011

A134886 INTERSECT A000040.

Formula rewritten by R. J. Mathar, Sep 09 2010

cp's OEIS Frontend

A175268 a(n)=floor(2^sqrt(n)).

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A175269 a(n) = floor(2^sqrt(n)) - floor(n^sqrt(2)).

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A180448 Primes of the form floor(k^sqrt(2)).

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