A224839 a(1) = 1 and a(n) is the smallest number greater than a(n-1) with no square difference with any preceding term.

1, 3, 6, 8, 11, 13, 16, 18, 21, 23, 35, 40, 45, 53, 58, 63, 66, 68, 73, 86, 96, 110, 120, 125, 128, 131, 133, 138, 143, 148, 151, 171, 178, 181, 183, 188, 193, 198, 205, 211, 216, 239, 244, 250, 256, 258, 261, 263, 268, 273

Offset: 1

Author

Jean-François Alcover, Sep 18 2013

Keywords

• nonn

Comments

The first 11 terms are identical to those of A210570.

This sequence represents the losing positions in the misère version of a one-heap nim game, where players remove a square number of objects (> 0) on their turn. - Kiran Ananthpur Bacche, Feb 23 2025

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030193, A210570, A010052.

Programs

Haskell

a224839 n = a224839_list !! (n-1)
a224839_list = f [1..] [] where
   f (x:xs) ys = if all ((== 0) . a010052) $ map (x -) ys
                    then x : f xs (x:ys) else f xs ys
-- Reinhard Zumkeller, May 02 2014

Maple

N:= 1000: # to get all terms <= N
V:= Vector(N):
Res:= NULL:
for m from 1 to N do
  if V[m] = 0 then
    V[m]:= 1;
    Res:= Res, m;
    for k from 1 to floor(sqrt(N-m)) do V[m+k^2]:= 1 od:
  fi
od:
Res; # Robert Israel, Nov 30 2016

Mathematica

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}]

Formula

a(n) >= A210570(n) by definition of the latter. - Charles R Greathouse IV, Nov 28 2024

a(n) = A030193(n-1) + 1. - Kiran Ananthpur Bacche, Feb 23 2025