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A273318 Numbers n such that n+k-1 is the sum of two nonzero squares in exactly k ways for all k = 1, 2, 3. 3

%I

%S 58472,79208,104616,150048,160848,205648,224648,234448,252808,259648,

%T 259920,294048,297448,387648,421648,433448,462976,488448,506248,

%U 563048,621448,683648,770976,790848,799648,837448,1008648,1040848,1084904,1186632,1195648,1205648,1212064

%N Numbers n such that n+k-1 is the sum of two nonzero squares in exactly k ways for all k = 1, 2, 3.

%C Numbers n such that n+k-1 is the sum of two nonzero squares in exactly 4-k ways for all k = 1, 2, 3 are 22984, 65600, 80800, 85544, ...

%H Robert Israel, <a href="/A273318/b273318.txt">Table of n, a(n) for n = 1..1095</a>

%e 58472 is a term because;

%e 58472 = 86^2 + 226^2.

%e 58473 = 48^2 + 237^2 = 147^2 + 192^2.

%e 58474 = 57^2 + 235^2 = 125^2 + 207^2 = 143^2 + 195^2.

%p N:= 10^6: # get all terms <= N-2

%p R:= Vector(N):

%p for x from 1 to floor(sqrt(N)) do

%p for y from 1 to min(x,floor(sqrt(N-x^2))) do

%p R[x^2+y^2]:= R[x^2+y^2]+1

%p od od:

%p count:= 0:

%p for n from 1 to N-2 do

%p if [R[n],R[n+1],R[n+2]] = [1,2,3] then

%p count:= count+1; A[count]:= n;

%p fi

%p od:

%p seq(A[i],i=1..count); # _Robert Israel_, May 19 2016

%o (PARI) is(n,k) = {nb = 0; lim = sqrtint(n); for (x=1, lim, if ((n-x^2 >= x^2) && issquare(n-x^2), nb++); ); nb == k; }

%o isok(n) = is(n,1) && is(n+1,2) && is(n+2,3);

%Y Cf. A000404, A025284, A025285, A025286.

%K nonn

%O 1,1

%A _Altug Alkan_, May 19 2016

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Last modified June 24 16:37 EDT 2021. Contains 345417 sequences. (Running on oeis4.)