A260709 Smallest nonsquare congruent to a square (mod k^2) for all k = 1..n.

2, 5, 13, 52, 241, 241, 436, 1009, 1009, 1009, 2641, 2641, 8089, 8089, 8089, 8089, 18001, 18001, 53881, 53881, 53881, 53881, 87481, 87481, 87481, 87481, 87481, 87481, 117049, 117049, 515761, 515761, 515761, 515761, 515761, 515761, 1083289, 1083289, 1083289, 1083289

Offset: 1

Author

M. F. Hasler, Nov 17 2015

Keywords

• nonn

Comments

A variant of A081650 which uses the remainder modulo k^2 instead of the congruence (mod k^2).

Suggested by Don Reble and R. Israel and the original title of A081650.

Links

• Robert Israel and Emmanuel Vantieghem, Table of n, a(n) for n = 1..81[Terms 1 through 70 were computed by R. Israel: terms 71 through 82 by E. Vantieghem. Nov 23 2015]
• R. Israel in reply to Don Reble, A081650, SeqFan list, Nov. 17, 2015

Crossrefs

Cf. A081650.

Programs

MATLAB

N = 2*10^8;  % to get all terms <= N
B = ones(1,N);
B([1:floor(sqrt(N))].^2) = 0;
m = 1;
while true
  nsq = ones(m^2,1);
  sqs = unique(mod([1:m^2/2].^2, m^2));
  sqs = [sqs(sqs > 0), m^2];
  nsq(sqs) = 0;
  S = nsq * ones(1,ceil(N/m^2));
  S = reshape(S,1,numel(S));
  B(S(1:N)>0) = 0;
  v = find(B,1,'first');
  if numel(v) == 0
    break
  end
  A(m) = v;
  m = m + 1;
end
A % Robert Israel, Nov 17 2015

Mathematica

(* to get the sequence up to B *)
VQR=Table[Union[Mod[Range[(n^2)/2]^2,n^2]],{n,2,17}];
Print[2];k=1;m=2;While[kEmmanuel Vantieghem, Nov 23 2013 *)

PARI

t=2;for(n=1,90, for(m=t,9e9,issquare(m)&&next; for(k=1,n,issquare(Mod(m,k^2))||next(2)); print1(t=m,",");break))