A184862 -id:A184862 - cp's OEIS frontend

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.

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

Clark Kimberling, Jan 23 2011

nonn

Cf. A184774, A184862, A184863.

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.)

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

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.

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