Displaying 1-10 of 14 results found.
Floor(n*(sqrt(13)+sqrt(5))).
+10
15
0, 5, 11, 17, 23, 29, 35, 40, 46, 52, 58, 64, 70, 75, 81, 87, 93, 99, 105, 110, 116, 122, 128, 134, 140, 146, 151, 157, 163, 169, 175, 181, 186, 192, 198, 204, 210, 216, 221, 227, 233, 239, 245, 251, 257, 262, 268, 274, 280, 286, 292
COMMENTS
Also integer part of n*5.8416192529..., where the constant is the largest root of x^4 -36*x^2 +64.
MATHEMATICA
With[{c = Sqrt[13] + Sqrt[5]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
PROG
(Magma) [Floor(n*(Sqrt(13)+Sqrt(5))): n in [0..60]];
Floor(n*(sqrt(13)+sqrt(3))).
+10
15
0, 5, 10, 16, 21, 26, 32, 37, 42, 48, 53, 58, 64, 69, 74, 80, 85, 90, 96, 101, 106, 112, 117, 122, 128, 133, 138, 144, 149, 154, 160, 165, 170, 176, 181, 186, 192, 197, 202, 208, 213, 218, 224, 229, 234, 240, 245, 250, 256, 261, 266
COMMENTS
Also integer part of n*5.3376020830..., where the constant is the largest root of x^4 -32*x^2 +100.
MATHEMATICA
With[{c = Sqrt[13] + Sqrt[3]}, Table[Floor[c n], {n, 0, 50}]] (* Harvey P. Dale, Apr 25 2011 *)
PROG
(Magma) [ Floor(n*(Sqrt(13)+Sqrt(3))): n in [0..60] ];
a(n) = floor(n*(sqrt(13)+sqrt(2))).
+10
15
0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 256, 261, 266, 271, 276
COMMENTS
a(n) = integer part of n*(sqrt(13)+sqrt(2)), where the constant is the largest root of x^4 -30*x^2 +121.
MATHEMATICA
With[{c = Sqrt[13] + Sqrt[2]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
PROG
(Magma) [Floor(n*(Sqrt(13)+Sqrt(2))): n in [0..60]];
(PARI) for(n=0, 50, print1(floor(n*(sqrt(13)+sqrt(2))), ", ")) \\ G. C. Greubel, Jul 05 2017
Floor(n*(sqrt(11)+sqrt(7))).
+10
3
0, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 292, 298, 304, 310, 316, 321, 327
COMMENTS
a(n) = integer part of n*(sqrt(11)+sqrt(7)), where the constant is the largest root of x^4 -36*x^2 +16.
MATHEMATICA
With[{c = Sqrt[11] + Sqrt[7]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
PROG
(Magma) [ Floor(n*(Sqrt(11)+Sqrt(7))): n in [0..60] ];
Floor(n*(sqrt(7)+sqrt(5))).
+10
1
0, 4, 9, 14, 19, 24, 29, 34, 39, 43, 48, 53, 58, 63, 68, 73, 78, 82, 87, 92, 97, 102, 107, 112, 117, 122, 126, 131, 136, 141, 146, 151, 156, 161, 165, 170, 175, 180, 185, 190, 195, 200, 205, 209, 214, 219, 224, 229, 234, 239, 244, 248, 253, 258, 263, 268, 273
COMMENTS
a(n) = integer part of n*(sqrt(7)+sqrt(5)), where the constant is the largest root of x^4 -24*x^2 +4.
MATHEMATICA
With[{c = Sqrt[7] + Sqrt[5]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
PROG
(Magma) [Floor(n*(Sqrt(7)+Sqrt(5))): n in [0..60]];
Floor(n*(sqrt(7)+sqrt(3))).
+10
1
0, 4, 8, 13, 17, 21, 26, 30, 35, 39, 43, 48, 52, 56, 61, 65, 70, 74, 78, 83, 87, 91, 96, 100, 105, 109, 113, 118, 122, 126, 131, 135, 140, 144, 148, 153, 157, 161, 166, 170, 175, 179, 183, 188, 192, 197, 201, 205, 210, 214, 218
COMMENTS
Also integer part of n*4.3778021186..., where the constant is the largest root of x^4 -20*x^2 +16.
MATHEMATICA
With[{c = Sqrt[7] + Sqrt[3]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
PROG
(Magma) [Floor(n*(Sqrt(7)+Sqrt(3))): n in [0..60]];
a(n) = floor(n*(sqrt(7) + sqrt(2))).
+10
1
0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202
COMMENTS
Also integer part of n*4.0599648734..., where the constant is the largest root of x^4 - 18*x^2 + 25.
MAPLE
a:=n->floor(n*(sqrt(7)+sqrt(2))): seq(a(n), n=0..60); # Muniru A Asiru, Sep 28 2018
MATHEMATICA
With[{c = Sqrt[7] + Sqrt[2]}, Floor[c Range[0, 60]]] (* Harvey P. Dale, Mar 23 2011 *)
PROG
(Magma) [Floor(n*(Sqrt(7)+Sqrt(2))): n in [0..60]];
(PARI) vector(60, n, n--; floor(n*(sqrt(7)+sqrt(2)))) \\ G. C. Greubel, Sep 28 2018
Floor(n*(sqrt(11)+sqrt(5))).
+10
1
0, 5, 11, 16, 22, 27, 33, 38, 44, 49, 55, 61, 66, 72, 77, 83, 88, 94, 99, 105, 111, 116, 122, 127, 133, 138, 144, 149, 155, 161, 166, 172, 177, 183, 188, 194, 199, 205, 211, 216, 222, 227, 233, 238, 244, 249, 255, 260, 266, 272, 277
COMMENTS
Also integer part of n*5.5526927678..., where the constant is the largest root of x^4 -32*x^2 +36.
MATHEMATICA
With[{c = Sqrt[11] + Sqrt[5]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
PROG
(Magma) [Floor(n*(Sqrt(11)+Sqrt(5))): n in [0..60]];
a(n) = floor(n*(sqrt(11)+sqrt(3))).
+10
1
0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 212, 217, 222, 227, 232, 237, 242, 247, 252
COMMENTS
Also integer part of n*5.0486755979..., where the constant is the largest root of x^4 -28*x^2 +64.
MATHEMATICA
With[{c = Sqrt[11] + Sqrt[3]}, Floor[c Range[0, 70]]] (* Vincenzo Librandi, Aug 01 2013 *)
PROG
(Magma) [Floor(n*(Sqrt(11)+Sqrt(3))): n in [0..60]];
a(n) = floor(n*(sqrt(11) + sqrt(2))).
+10
1
0, 4, 9, 14, 18, 23, 28, 33, 37, 42, 47, 52, 56, 61, 66, 70, 75, 80, 85, 89, 94, 99, 104, 108, 113, 118, 123, 127, 132, 137, 141, 146, 151, 156, 160, 165, 170, 175, 179, 184, 189, 193, 198, 203, 208, 212, 217, 222, 227, 231, 236
COMMENTS
Also integer part of n*4.7308383527..., where the constant is the largest root of x^4 - 26*x^2 + 81.
MAPLE
a:=n->floor(n*(sqrt(11)+sqrt(2))): seq(a(n), n=0..60); # Muniru A Asiru, Sep 28 2018
MATHEMATICA
With[{c=Sqrt[11]+Sqrt[2]}, Table[Floor[c n], {n, 0, 50}]] (* Harvey P. Dale, Mar 12 2011 *)
PROG
(Magma) [Floor(n*(Sqrt(11)+Sqrt(2))): n in [0..60]];
(PARI) vector(60, n, n--; floor(n*(sqrt(11)+sqrt(2)))) \\ G. C. Greubel, Sep 28 2018
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