A260709 - OEIS

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

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OFFSET

1,1

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

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[k<B, k++; m--; flag=0; While[flag==0, Label[m$]; m++; If[!IntegerQ[Sqrt[m]], j=1; While[j<k, j++; If[! MemberQ[VQR[[j-1]], Mod[m, j^2]], Goto[m$]]]; If[j==k, Print[m]; flag=1]]]](* Emmanuel Vantieghem, Nov 23 2013 *)

PROG

(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))

(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

CROSSREFS

Cf. A081650.

Sequence in context: A303792 A059103 A365709 * A112836 A353719 A353722

Adjacent sequences: A260706 A260707 A260708 * A260710 A260711 A260712

KEYWORD

nonn

AUTHOR

M. F. Hasler, Nov 17 2015

STATUS

approved