

A245289


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


3



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
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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(m1)+ 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, #v1, if(2*v[k] == v[k1]+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

JuriStepan Gerasimov, Jul 16 2014


STATUS

approved



