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%I #22 May 30 2016 18:24:12
%S 1,15,39,89,161,271,415,17,37,91,159,273,413,19,35,93,157,275,411,21,
%T 33,95,155,277,409,23,31,97,153,279,407,25,29,99,151,281,405,27,101,
%U 149,283,403,621,65,63,187,245,5,11,43,85,165,267,419,13,3,51,77,173,259,427,597,861,163,87,41,209,223,463,561,125
%N With a(1) = 1, a(n) is the smallest number not already in the sequence such that the arithmetic mean of two neighboring terms is a cube.
%C Believed to be a permutation of the odd integers.
%C A259603(n) = (a(n) + a(n+1)) / 2; a(A259537(n)) = 2*n-1. - _Reinhard Zumkeller_, Jun 30 2015
%C The scatter-plot shows interesting helix-like lenticular structures. - _Antti Karttunen_, May 29 2016
%H Reinhard Zumkeller, <a href="/A259429/b259429.txt">Table of n, a(n) for n = 1..10000</a>
%t a = {1}; Do[k = 1; While[Or[MemberQ[a, k], !IntegerQ@ Power[Mean[{a[[i - 1]], k}], 1/3]], k++]; AppendTo[a, k], {i, 2, 120}]; a (* _Michael De Vlieger_, May 29 2016 *)
%o (PARI) v=[1]; n=1; while(#v<200, s=(n+v[#v])/2; if(type(s)=="t_INT", if(ispower(s,3)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0)); n++); v
%o (Haskell)
%o import Data.List (delete)
%o a259429 n = a259429_list !! (n-1)
%o a259429_list = 1 : f 1 [3, 5 ..] where
%o f x zs = g zs where
%o g (y:ys) = if a010057 ((x + y) `div` 2) == 1
%o then y : f y (delete y zs) else g ys
%o -- _Reinhard Zumkeller_, Jun 29 2015
%Y Cf. A259260, A086517, A175428.
%Y Cf. A010057, A005408, A259537.
%Y Cf. A259603, A259565, A259542.
%K nonn,look
%O 1,2
%A _Derek Orr_, Jun 26 2015
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