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

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

Author

Clark Kimberling, Jan 23 2011

Keywords

• nonn

Comments

See "conjecture generalized" at A184774.

Crossrefs

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

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