A259565 - OEIS

%I #7 Jun 30 2015 17:12:12

%S 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 47,55,51,59,57,53,61,63,67,65,69,71,75,73,81,77,79,85,87,83,89,93,95,

%U 91,97,105,99,103,101,109,111,107,113,115,121,117,119,125,129

%N 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 A259605(n) = (a(n) + a(n+1)) / 2;

%C conjecture: sequence is a permutation of the odd numbers;

%C a(A259570(n)) = 2*n-1.

%H Reinhard Zumkeller, <a href="/A259565/b259565.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o import Data.List (delete)

%o a259565 n = a259565_list !! (n-1)

%o a259565_list = 1 : f 1 [3, 5 ..] where

%o    f x zs = g zs where

%o      g (y:ys) = if a008966 ((x + y) `div` 2) == 1

%o                    then y : f y (delete y zs) else g ys

%Y Cf. A086517, A259260, A259429, A259542, A008966, A005117, A005408, A259570.

%Y Cf. A259605.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jun 30 2015