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A268330 Least squarefree number differing by more than n from any other squarefree number. 6
1, 17, 26, 2526, 5876126, 8061827, 8996188226, 2074150570370 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

1.8*10^12 < a(7) <= 10735237201449 - Robert Israel, Mar 18 2016

a(8) > 5*10^12. - Giovanni Resta, Apr 11 2016

LINKS

Table of n, a(n) for n=0..7.

EXAMPLE

a(2) = 26 because 26 is squarefree but 24,25,27,28 are not.

MATHEMATICA

(* implementation assumes a(n) is increasing *)

nsfRun[n_]:=Module[{i=n}, While[!SquareFreeQ[i], i++]; i-n]

a268330[{low_, high_}, width_]:=Module[{k=width, i, next, r, s, list={}}, For[i=low, i<=high, i+=next, r=nsfRun[i]; If[r<k, next=r+1, s=nsfRun[i+r+1]; If[s<k, next=r+s+2, If[s==k, next=r+s+2, next=r+1]; AppendTo[list, {i, i+r, i+r+s}]; k++]]]; list] /; width>0 (* Hartmut F. W. Hoft, Mar 15 2016 *)

a268330[{0, 10000000}, 1]]] (* computes a(1)...a(5) *)

PROG

(MATLAB)

B = 10^8; % blocks of size B

nB = 1000; % nB blocks

A = [1];

P = primes(floor(sqrt(nB*B)));

mmax = 1;

i0 = 1;

for k = 0:nB-1  % search squarefrees from i0+1 to i0 + B

  V = true(1, B);

  for i = 1:numel(P)

    p = P(i);

    V([(p^2 - mod(i0, p^2)):p^2:B]) = false;

  end

  SF = find(V) + i0;

  DSF = SF(2:end) - SF(1:end-1);

  i0 = SF(end-2);

  M = min(DSF(1:end-1), DSF(2:end));

  newmax = max(mmax, max(M));

  for i = mmax+1:newmax

    A(i) = SF(1 + find(M>=i, 1, 'first'));

  end

  mmax = newmax;

end

for i=1:mmax

  fprintf('%d ', A(i));

end

fprintf('\n');  % Robert Israel, Mar 16 2016

CROSSREFS

Cf. A073247, A268331, A268332, A268333, A268334.

Sequence in context: A154277 A140150 A166658 * A221282 A033702 A000797

Adjacent sequences:  A268327 A268328 A268329 * A268331 A268332 A268333

KEYWORD

nonn,more

AUTHOR

Christopher E. Thompson, Feb 01 2016

EXTENSIONS

a(6) from Hartmut F. W. Hoft, Mar 15 2016

a(7) from Giovanni Resta, Apr 11 2016

STATUS

approved

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Last modified January 17 16:31 EST 2021. Contains 340246 sequences. (Running on oeis4.)