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 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. 6
 1, 3, 7, 5, 9, 11, 15, 13, 17, 21, 23, 19, 25, 27, 31, 29, 33, 35, 39, 37, 41, 43, 49, 45, 47, 55, 51, 59, 57, 53, 61, 63, 67, 65, 69, 71, 75, 73, 81, 77, 79, 85, 87, 83, 89, 93, 95, 91, 97, 105, 99, 103, 101, 109, 111, 107, 113, 115, 121, 117, 119, 125, 129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A259605(n) = (a(n) + a(n+1)) / 2; conjecture: sequence is a permutation of the odd numbers; a(A259570(n)) = 2*n-1. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 PROG (Haskell) import Data.List (delete) a259565 n = a259565_list !! (n-1) a259565_list = 1 : f 1 [3, 5 ..] where    f x zs = g zs where      g (y:ys) = if a008966 ((x + y) `div` 2) == 1                    then y : f y (delete y zs) else g ys CROSSREFS Cf. A086517, A259260, A259429, A259542, A008966, A005117, A005408, A259570. Cf. A259605. Sequence in context: A019809 A305741 A021270 * A113910 A264983 A265341 Adjacent sequences:  A259562 A259563 A259564 * A259566 A259567 A259568 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jun 30 2015 STATUS approved

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Last modified January 23 10:50 EST 2020. Contains 331171 sequences. (Running on oeis4.)