A258767 - OEIS

%I #10 Jun 11 2015 17:40:25

%S 1,7,14,2,4,3,6,8,10,5,12,9,13,16,18,15,20,21,22,11,23,36,24,26,28,29,

%T 47,46,30,25,35,40,32,34,17,19,33,27,31,42,38,41,37,39,45,48,44,50,49,

%U 43,51,54,52,56,58,59,62,60,55,65,70,63,57,66,64,68,72,69,67,81,75,78,71,53,79,97,96,74

%N With a(1) = 1, a(n) is the smallest number not already in the sequence such that a(n)^2 + a(n-1)^2 is not squarefree.

%C Believed to be a permutation of the natural numbers.

%H Reinhard Zumkeller, <a href="/A258767/b258767.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) v=[1]; n=1; while(n<100, if(!issquarefree(n^2+v[#v]^2)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v

%o (Haskell)

%o import Data.List (delete)

%o a258767 n = a258767_list !! (n-1)

%o a258767_list = 1 : f 1 [2..] where

%o    f x zs = g zs where

%o      g (y:ys) | a008966 (x^2 + y^2) == 1 = g ys

%o               | otherwise = y : f y (delete y zs)

%o -- _Reinhard Zumkeller_, Jun 11 2015

%Y Cf. A256271, A075380.

%Y Cf. A258768 (fixed points).

%Y Cf. A008966, A258827 (putative inverse).

%K nonn

%O 1,2

%A _Derek Orr_, Jun 09 2015