A245289 Balanced squarefrees (of order one): squarefree numbers which are the average of the previous squarefree number and the following squarefree number.

2, 6, 14, 17, 19, 22, 26, 30, 34, 38, 42, 53, 55, 58, 66, 70, 78, 86, 89, 91, 94, 102, 106, 110, 114, 130, 138, 142, 158, 161, 163, 166, 170, 178, 182, 186, 194, 197, 199, 202, 210, 214, 218, 222, 230, 233, 235, 238, 249

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 16 2014

Keywords

• nonn

Comments

All even a(n) are numbers of the form 4k + 2 (as with all even squarefree numbers).

Examples

			2 is in this sequence because it is squarefree and the average of the previous squarefree number 1 and the following squarefree number 3.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A240475.

Programs

Mathematica

With[{sqfr=Select[Range[500],SquareFreeQ]},Transpose[Select[ Partition[ sqfr,3,1],(#[[1]]+#[[3]])/2==#[[2]]&]][[2]]] (* Harvey P. Dale, Dec 15 2014 *)

PARI

v = select(n->issquarefree(n), vector(300, n, n));
for(k=2, #v-1, if(2*v[k] == v[k-1]+v[k+1], print1(v[k], ", "))) \\ Colin Barker, Jul 17 2014

Formula

With b(m) = A005117(m), m >= 2, this is the sequence of the increasingly ordered members of the set {b(m): b(m) = (b(m-1)+ b(m+1))/2}. - Wolfdieter Lang, Jul 25 2014