A184860 -id:A184860 - cp's OEIS frontend

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

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

Clark Kimberling, Jan 23 2011

nonn

See "conjecture generalized" at A184774.

			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,...

Cf. A184774, A184859, A184860, A184861.

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 *)

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

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 21, 22, 23, 24, 25, 28, 30, 32, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 51, 52, 53, 54, 55, 57, 59, 61, 62, 63, 64, 66, 68, 70, 71, 72, 73, 75, 76, 79, 80, 81, 82, 86, 89, 90, 92, 93, 96, 98, 99, 101, 102, 103, 105, 107, 109, 111, 112, 115, 116, 118, 120, 122, 124, 125, 126, 127, 130, 131, 132, 133, 134, 136, 137, 140, 141, 144, 147, 149, 151, 153, 154, 156, 157, 158, 159, 161, 162, 164

Offset: 1

Clark Kimberling, Jan 23 2011

nonn

			See A184859.

Cf. A184859, A184864.

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. *)

cp's OEIS Frontend

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

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