A184864 -id:A184864 - cp's OEIS frontend

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.

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. *)

A184862 Primes of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2.

Original entry on oeis.org

7, 17, 41, 43, 59, 67, 101, 103, 109, 127, 137, 151, 179, 211, 229, 263, 271, 281, 313, 331, 347, 373, 389, 397, 431, 433, 439, 449, 457, 467, 491, 499, 509, 541, 569, 577, 593, 601, 617, 619, 643, 653, 661, 677, 719, 727, 761, 787, 797, 821, 823, 829, 839, 857, 863, 881, 907, 941, 967, 983, 991, 1009, 1033, 1049, 1051, 1069, 1093, 1109, 1117, 1151, 1153, 1187, 1193, 1213, 1229, 1237, 1279, 1289, 1297, 1321, 1373, 1381, 1399, 1423, 1433, 1439, 1483, 1499, 1543, 1549, 1559, 1567

Offset: 1

Clark Kimberling, Jan 23 2011

nonn

See "conjecture generalized" at A184774.

Cf. A007064, A184774, A184859, A184863, A184864.

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.)
With[{gr=GoldenRatio},Select[Table[Floor[n+n*gr-gr/2],{n,2000}],PrimeQ]] (* Harvey P. Dale, Sep 18 2024 *)

A184863 Numbers k such that floor(n+nr-r/2) are prime, where r=(1+sqrt(5))/2.

Original entry on oeis.org

3, 7, 16, 17, 23, 26, 39, 40, 42, 49, 53, 58, 69, 81, 88, 101, 104, 108, 120, 127, 133, 143, 149, 152, 165, 166, 168, 172, 175, 179, 188, 191, 195, 207, 218, 221, 227, 230, 236, 237, 246, 250, 253, 259, 275, 278, 291, 301, 305, 314, 315, 317, 321, 328, 330, 337, 347, 360, 370, 376, 379, 386, 395, 401, 402, 409, 418, 424, 427, 440, 441, 454, 456, 464, 470, 473, 489, 493, 496, 505, 525, 528, 535, 544, 548, 550, 567, 573, 590, 592, 596, 599

Offset: 1

Clark Kimberling, Jan 23 2011

nonn

Cf. A184862, A184864.

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.)
With[{gr=GoldenRatio},Select[Range[600],PrimeQ[Floor[#+gr*#-gr/2]]&]] (* Harvey P. Dale, Jul 06 2025 *)

cp's OEIS Frontend

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.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A184862 Primes of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A184863 Numbers k such that floor(n+nr-r/2) are prime, where r=(1+sqrt(5))/2.

Views

Author

Keywords

Crossrefs

Programs

Mathematica