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

1,1

Comments

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

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A005117, A240475.

Sequence in context: A212719 A145213 A050859 * A065196 A295326 A032483

Adjacent sequences: A245286 A245287 A245288 * A245290 A245291 A245292

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 16 2014

Status

approved