A184807 -id:A184807 - cp's OEIS frontend

A184804 Numbers m such that prime(m) is of the form floor(k*sqrt(5)); complement of A184807.

1, 5, 6, 7, 10, 11, 16, 19, 20, 21, 24, 28, 29, 31, 32, 35, 38, 39, 42, 46, 48, 52, 53, 55, 56, 59, 60, 61, 65, 66, 68, 71, 74, 77, 80, 83, 84, 87, 91, 93, 94, 96, 97, 98, 99, 100, 101, 103, 109, 110, 113, 114, 116, 117, 120, 121, 122, 123, 130, 133, 136, 137, 138, 140, 141, 144, 145, 150, 152, 153, 154, 155, 157, 160, 165, 166, 168, 171, 172, 174, 175, 182, 183, 184, 186, 189, 190, 191, 193, 195, 200, 201, 204, 207, 208, 212, 213, 215, 216

Offset: 1

Clark Kimberling, Jan 22 2011

nonn

			See A184802.

Cf. A184802, A184803, A184804, A184807.

Mathematica
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(See A184802.)
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A184802 Primes of the form floor(k*sqrt(5)).

Original entry on oeis.org

2, 11, 13, 17, 29, 31, 53, 67, 71, 73, 89, 107, 109, 127, 131, 149, 163, 167, 181, 199, 223, 239, 241, 257, 263, 277, 281, 283, 313, 317, 337, 353, 373, 389, 409, 431, 433, 449, 467, 487, 491, 503, 509, 521, 523, 541, 547, 563, 599, 601, 617, 619, 641, 643

Offset: 1

Clark Kimberling, Jan 22 2011

nonn

See A184774.

			The sequence U(n)=floor(n*sqrt(5)) begins with
2,4,6,8,11,13,15,17,20,22,24,26,29,...,
which includes the primes U(1)=2, U(5)=11,...

Cf. A184774, A022839, A108598, A184802, A184803, A184804, A184805, A184806, A184807.

r=5^(1/2); s=r/(r-1);
a[n_]:=Floor [n*r];  (* A022839 *)
b[n_]:=Floor [n*s];  (* A108598 *)
Table[a[n],{n,1,120}]
t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4
t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5
t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,300}];t6
(* The lists t1, t2, t3, t4, t5, t6 match the sequences
A184802, A184803, A184804, A184805, A184806, A184807. *)

for(k=1,300,isprime(p=sqrtint(k^2*5))&&print1(p",")) \\ M. F. Hasler, Aug 26 2014

A184806 Numbers k such that floor(k*s) is prime, where s = (5 + sqrt(5))/4.

Original entry on oeis.org

2, 3, 4, 11, 13, 21, 23, 24, 26, 33, 34, 44, 46, 54, 56, 57, 63, 76, 77, 84, 87, 96, 99, 106, 107, 109, 117, 126, 127, 129, 139, 149, 150, 162, 170, 172, 183, 192, 193, 199, 203, 210, 212, 220, 222, 232, 233, 243, 245, 253, 255, 256, 265, 276, 308, 315, 316, 319, 325, 328, 336, 339, 349, 358, 361, 378, 382, 388, 392, 398, 402, 409, 411, 419, 421, 441, 454, 455, 464, 472, 474, 475, 485, 504, 514, 518, 524, 527, 535, 537, 548, 558, 560, 570, 580, 581, 587, 588, 591

Offset: 1

Clark Kimberling, Jan 22 2011

nonn

			See A184802.

Cf. A108598, A184802, A184807.

(See A184802.)
With[{s=(5+Sqrt[5])/4},Select[Range[600],PrimeQ[Floor[#*s]]&]] (* Harvey P. Dale, Jul 04 2014 *)

A184805 Primes of the form floor(k*s), where s=(5+sqrt(5))/4.

Original entry on oeis.org

3, 5, 7, 19, 23, 37, 41, 43, 47, 59, 61, 79, 83, 97, 101, 103, 113, 137, 139, 151, 157, 173, 179, 191, 193, 197, 211, 227, 229, 233, 251, 269, 271, 293, 307, 311, 331, 347, 349, 359, 367, 379, 383, 397, 401, 419, 421, 439, 443, 457, 461, 463, 479, 499, 557, 569, 571, 577, 587, 593, 607, 613, 631, 647, 653, 683, 691, 701, 709, 719, 727, 739, 743, 757, 761, 797, 821, 823, 839, 853, 857, 859, 877, 911, 929, 937, 947, 953, 967, 971, 991, 1009, 1013, 1031, 1049, 1051, 1061, 1063, 1069

Offset: 1

Clark Kimberling, Jan 22 2011

nonn

			See A184802.

Cf. A184774, A108598, A184802, A184806, A184807.

(See A184802.)
With[{s=(5+Sqrt[5])/4},Select[Table[Floor[s*n],{n,600}],PrimeQ]] (* Harvey P. Dale, Feb 04 2015 *)

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A184804 Numbers m such that prime(m) is of the form floor(k*sqrt(5)); complement of A184807.

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A184802 Primes of the form floor(k*sqrt(5)).

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A184806 Numbers k such that floor(k*s) is prime, where s = (5 + sqrt(5))/4.

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Examples

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Mathematica

A184805 Primes of the form floor(k*s), where s=(5+sqrt(5))/4.

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica