A259429 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.

1, 15, 39, 89, 161, 271, 415, 17, 37, 91, 159, 273, 413, 19, 35, 93, 157, 275, 411, 21, 33, 95, 155, 277, 409, 23, 31, 97, 153, 279, 407, 25, 29, 99, 151, 281, 405, 27, 101, 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

Offset: 1

Author

Derek Orr, Jun 26 2015

Keywords

• nonn
• look

Comments

Believed to be a permutation of the odd integers.

A259603(n) = (a(n) + a(n+1)) / 2; a(A259537(n)) = 2*n-1. - Reinhard Zumkeller, Jun 30 2015

The scatter-plot shows interesting helix-like lenticular structures. - Antti Karttunen, May 29 2016

Links

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

Crossrefs

Cf. A259260, A086517, A175428.

Cf. A010057, A005408, A259537.

Cf. A259603, A259565, A259542.

Programs

Haskell

import Data.List (delete)
a259429 n = a259429_list !! (n-1)
a259429_list = 1 : f 1 [3, 5 ..] where
   f x zs = g zs where
     g (y:ys) = if a010057 ((x + y) `div` 2) == 1
                   then y : f y (delete y zs) else g ys
-- Reinhard Zumkeller, Jun 29 2015

Mathematica

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 *)

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