cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A184807 Numbers m such that prime(m) is of the form floor(k*s), where s=(5+sqrt(5))/4; complement of A184804.

Original entry on oeis.org

2, 3, 4, 8, 9, 12, 13, 14, 15, 17, 18, 22, 23, 25, 26, 27, 30, 33, 34, 36, 37, 40, 41, 43, 44, 45, 47, 49, 50, 51, 54, 57, 58, 62, 63, 64, 67, 69, 70, 72, 73, 75, 76, 78, 79, 81, 82, 85, 86, 88, 89, 90, 92, 95, 102, 104, 105, 106, 107, 108, 111, 112, 115, 118, 119, 124, 125, 126, 127, 128, 129, 131, 132, 134, 135, 139, 142, 143, 146, 147, 148, 149, 151, 156, 158, 159, 161, 162, 163, 164, 167, 169, 170, 173, 176, 177, 178, 179, 180
Offset: 1

Views

Author

Clark Kimberling, Jan 22 2011

Keywords

Examples

			See A184802.

Crossrefs

Cf. A184802, A184804, A184805, A184806.

Programs

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

Views

Author

Clark Kimberling, Jan 22 2011

Keywords

Comments

See A184774.

Examples

			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,...

Crossrefs

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

Programs

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

A184803 Numbers k such that floor(k*sqrt(5)) is prime.

Original entry on oeis.org

1, 5, 6, 8, 13, 14, 24, 30, 32, 33, 40, 48, 49, 57, 59, 67, 73, 75, 81, 89, 100, 107, 108, 115, 118, 124, 126, 127, 140, 142, 151, 158, 167, 174, 183, 193, 194, 201, 209, 218, 220, 225, 228, 233, 234, 242, 245, 252, 268, 269, 276, 277, 287, 288, 295, 296, 301, 303, 328, 336, 344, 346, 352, 362, 363, 370, 371, 386, 394, 395, 397, 406, 411, 421, 437, 440, 446, 456, 457, 462, 465, 488, 489, 491, 496, 505, 515, 516, 524, 531, 547, 550, 559, 572, 574, 582, 583, 590, 591
Offset: 1

Views

Author

Clark Kimberling, Jan 22 2011

Keywords

Examples

			See A184802.

Crossrefs

Cf. A022839, A184802, A184803, A184804.

Programs

Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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