A259260 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 square.

1, 7, 11, 21, 29, 3, 5, 13, 19, 31, 41, 9, 23, 27, 45, 53, 75, 87, 113, 15, 17, 33, 39, 59, 69, 93, 35, 37, 61, 67, 95, 105, 57, 71, 91, 109, 133, 155, 183, 209, 79, 49, 151, 137, 25, 47, 51, 77, 85, 43, 55, 73, 89, 111, 131, 157, 181, 107, 135, 65, 63, 99, 101, 141, 147, 191, 97, 103, 139, 149, 189, 203, 247, 145

Offset: 1

Author

Derek Orr, Jun 22 2015

Keywords

• nonn

Comments

Conjectured to be a permutation of the odd numbers.

A259602(n) = (a(n) + a(n+1)) / 2; a(A259526(n)) = 2*n-1. - Reinhard Zumkeller, Jun 29 2015

Links

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

Crossrefs

Cf. A034175, A086517.

Cf. A010052, A005408.

Cf. A259602, A259565, A259429, A259542.

Programs

Haskell

import Data.List (delete)
a259260 n = a259260_list !! (n-1)
a259260_list = 1 : f 1 [3, 5 ..] where
   f x zs = g zs where
     g (y:ys) = if a010052 ((x + y) `div` 2) == 1
                   then y : f y (delete y zs) else g ys
-- Reinhard Zumkeller, Jun 29 2015

Mathematica

s={1}; Do[n = Last@ s; a=2; While[(b = 2*a^2 - n) <= 0 || MemberQ[s, b], a++]; AppendTo[s, b], {100}]; s (* Giovanni Resta, Jun 23 2015 *)

PARI

v=[1];n=1;while(#v<100,s=(n+v[#v])/2;if(type(s)=="t_INT",if(issquare(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0));n++);v