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.

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

Offset: 1

Author

Reinhard Zumkeller, Jun 30 2015

Keywords

• nonn

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

Crossrefs

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

Cf. A259605.

Programs

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