

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
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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*n1.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


PROG

(Haskell)
import Data.List (delete)
a259565 n = a259565_list !! (n1)
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



