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A184862 Primes of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2. 3


%S 7,17,41,43,59,67,101,103,109,127,137,151,179,211,229,263,271,281,313,

%T 331,347,373,389,397,431,433,439,449,457,467,491,499,509,541,569,577,

%U 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

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

%C See "conjecture generalized" at A184774.

%t r=(1+5^(1/2))/2;

%t a[n_]:=Floor [n+n*r-r/2];

%t Table[a[n],{n,1,120}] (* A007064 *)

%t t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1

%t t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2

%t t3={}; Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3

%t *( Lists t1, t2, t3 match A184862, A184863, A184864.)

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

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 23 2011

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Last modified June 19 17:25 EDT 2021. Contains 345144 sequences. (Running on oeis4.)