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%I #15 Dec 15 2014 07:37:56
%S 2,6,14,17,19,22,26,30,34,38,42,53,55,58,66,70,78,86,89,91,94,102,106,
%T 110,114,130,138,142,158,161,163,166,170,178,182,186,194,197,199,202,
%U 210,214,218,222,230,233,235,238,249
%N Balanced squarefrees (of order one): squarefree numbers which are the average of the previous squarefree number and the following squarefree number.
%C All even a(n) are numbers of the form 4k + 2 (as with all even squarefree numbers).
%H Jens Kruse Andersen, <a href="/A245289/b245289.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%e 2 is in this sequence because it is squarefree and the average of the previous squarefree number 1 and the following squarefree number 3.
%t With[{sqfr=Select[Range[500],SquareFreeQ]},Transpose[Select[ Partition[ sqfr,3,1],(#[[1]]+#[[3]])/2==#[[2]]&]][[2]]] (* _Harvey P. Dale_, Dec 15 2014 *)
%o (PARI)
%o v = select(n->issquarefree(n), vector(300, n, n));
%o for(k=2, #v-1, if(2*v[k] == v[k-1]+v[k+1], print1(v[k], ", "))) \\ _Colin Barker_, Jul 17 2014
%Y Cf. A005117, A240475.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Jul 16 2014
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