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.

A184864 Numbers m such that prime(m) is of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2; complement of A184861.

Original entry on oeis.org

4, 7, 13, 14, 17, 19, 26, 27, 29, 31, 33, 36, 41, 47, 50, 56, 58, 60, 65, 67, 69, 74, 77, 78, 83, 84, 85, 87, 88, 91, 94, 95, 97, 100, 104, 106, 108, 110, 113, 114, 117, 119, 121, 123, 128, 129, 135, 138, 139, 142, 143, 145, 146, 148, 150, 152, 155, 160, 163, 166, 167, 169, 174, 176, 177, 180, 183, 186, 187, 190, 191, 195, 196, 198, 201, 203, 207, 209, 211, 216, 220, 221, 222, 224, 227, 228, 235, 239, 243, 244, 246, 247
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Crossrefs

Cf. A184774, A184862, A184863.

Programs

  • Mathematica
    r=(1+5^(1/2))/2;
a[n_]:=Floor [n+n*r-r/2];
Table[a[n], {n, 1, 120}]  (* A007064 *)
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
*( Lists t1, t2, t3 match A184862, A184863, A184864.)

A184859 Primes of the form floor(kr+h), where r=(1+sqrt(5))/2 and h=1/2.

Original entry on oeis.org

2, 3, 5, 11, 13, 19, 23, 29, 31, 37, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 113, 131, 139, 149, 157, 163, 167, 173, 181, 191, 193, 197, 199, 223, 227, 233, 239, 241, 251, 257, 269, 277, 283, 293, 307, 311, 317, 337, 349, 353, 359, 367, 379, 383, 401, 409, 419, 421, 443, 461, 463, 479, 487, 503, 521, 523, 547, 557, 563, 571, 587, 599, 607, 613, 631, 641, 647, 659, 673, 683, 691, 701, 709, 733, 739, 743, 751, 757, 769, 773, 809, 811, 827, 853, 859, 877, 883, 887, 911, 919, 929, 937, 947, 953, 971
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Comments

See "conjecture generalized" at A184774.

Examples

			The sequence U(n)=floor(n*r+h) begins with
2,3,5,6,8,10,11,13,15,16,18,19,...,
which includes the primes U(1)=2, U(2)=3,...

Crossrefs

Cf. A184774, A184859, A184860, A184861.

Programs

  • Mathematica
    r=(1+5^(1/2))/2; h=1/2;s=r/(r-1);
a[n_]:=Floor [n*r+h];
Table[a[n],{n,1,120}]  (* A007067 *)
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
(* Lists t1, t2, t3 match A184859, A184860, A184861. *)
Select[Floor[GoldenRatio*Range[600]+1/2],PrimeQ] (* Harvey P. Dale, Jan 02 2013 *)

A184860 Numbers k such that floor(nr+h) is prime, where r=(1+sqrt(5))/2 and h=1/2.

Original entry on oeis.org

1, 2, 3, 7, 8, 12, 14, 18, 19, 23, 29, 33, 38, 44, 45, 49, 51, 55, 60, 66, 70, 81, 86, 92, 97, 101, 103, 107, 112, 118, 119, 122, 123, 138, 140, 144, 148, 149, 155, 159, 166, 171, 175, 181, 190, 192, 196, 208, 216, 218, 222, 227, 234, 237, 248, 253, 259, 260, 274, 285, 286, 296, 301, 311, 322, 323, 338, 344, 348, 353, 363, 370, 375, 379, 390, 396, 400, 407, 416, 422, 427, 433, 438, 453, 457, 459, 464, 468, 475, 478, 500, 501, 511, 527, 531, 542, 546, 548, 563, 568, 574, 579, 585, 589, 600
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Examples

			See A184859.

Crossrefs

Cf. A184859, A184861.

Programs

  • Mathematica
    r=(1+5^(1/2))/2; h=1/2; s=r/(r-1);
a[n_]:=Floor [n*r+h];
Table[a[n], {n, 1, 120}]  (* A007067 *)
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
(* Lists t1, t2, t3 match A184859, A184860, A184861. *)
Showing 1-3 of 3 results.

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