cp's OEIS Frontend

A259565 a(1) = 1, for n > 1 a(n) = smallest number not already in the sequence such that the arithmetic mean of two neighboring terms is a squarefree number.

%I A259565 #7 Jun 30 2015 17:12:12
%S A259565 1,3,7,5,9,11,15,13,17,21,23,19,25,27,31,29,33,35,39,37,41,43,49,45,
%T A259565 47,55,51,59,57,53,61,63,67,65,69,71,75,73,81,77,79,85,87,83,89,93,95,
%U A259565 91,97,105,99,103,101,109,111,107,113,115,121,117,119,125,129
%N A259565 a(1) = 1, for n > 1 a(n) = smallest number not already in the sequence such that the arithmetic mean of two neighboring terms is a squarefree number.
%C A259565 A259605(n) = (a(n) + a(n+1)) / 2;
%C A259565 conjecture: sequence is a permutation of the odd numbers;
%C A259565 a(A259570(n)) = 2*n-1.
%H A259565 Reinhard Zumkeller, <a href="/A259565/b259565.txt">Table of n, a(n) for n = 1..10000</a>
%o A259565 (Haskell)
%o A259565 import Data.List (delete)
%o A259565 a259565 n = a259565_list !! (n-1)
%o A259565 a259565_list = 1 : f 1 [3, 5 ..] where
%o A259565    f x zs = g zs where
%o A259565      g (y:ys) = if a008966 ((x + y) `div` 2) == 1
%o A259565                    then y : f y (delete y zs) else g ys
%Y A259565 Cf. A086517, A259260, A259429, A259542, A008966, A005117, A005408, A259570.
%Y A259565 Cf. A259605.
%K A259565 nonn
%O A259565 1,2
%A A259565 _Reinhard Zumkeller_, Jun 30 2015