A224839 - OEIS

%I #26 Nov 28 2024 21:29:50

%S 1,3,6,8,11,13,16,18,21,23,35,40,45,53,58,63,66,68,73,86,96,110,120,

%T 125,128,131,133,138,143,148,151,171,178,181,183,188,193,198,205,211,

%U 216,239,244,250,256,258,261,263,268,273

%N a(1) = 1 and a(n) is the smallest number greater than a(n-1) with no square difference with any preceding term.

%C The first 11 terms are identical to those of A210570.

%H Jean-François Alcover, <a href="/A224839/b224839.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) >= A210570(n) by definition of the latter. - _Charles R Greathouse IV_, Nov 28 2024

%p N:= 1000: # to get all terms <= N

%p V:= Vector(N):

%p Res:= NULL:

%p for m from 1 to N do

%p   if V[m] = 0 then

%p     V[m]:= 1;

%p     Res:= Res, m;

%p     for k from 1 to floor(sqrt(N-m)) do V[m+k^2]:= 1 od:

%p   fi

%p od:

%p Res; # _Robert Israel_, Nov 30 2016

%t a[1] = 1; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, If[FreeQ[k - Array[a, n-1], d_ /; IntegerQ[Sqrt[d]]], Return[k]]]; Table[a[n], {n, 1, 40}]

%o (Haskell)

%o a224839 n = a224839_list !! (n-1)

%o a224839_list = f [1..] [] where

%o    f (x:xs) ys = if all ((== 0) . a010052) $ map (x -) ys

%o                     then x : f xs (x:ys) else f xs ys

%o -- _Reinhard Zumkeller_, May 02 2014

%Y Cf. A210570.

%Y Cf. A010052.

%K nonn

%O 1,2

%A _Jean-François Alcover_, Sep 18 2013