A184863 -id:A184863 - 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.)

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 *)

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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