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A273318
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Numbers n such that n+k-1 is the sum of two nonzero squares in exactly k ways for all k = 1, 2, 3.
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3
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58472, 79208, 104616, 150048, 160848, 205648, 224648, 234448, 252808, 259648, 259920, 294048, 297448, 387648, 421648, 433448, 462976, 488448, 506248, 563048, 621448, 683648, 770976, 790848, 799648, 837448, 1008648, 1040848, 1084904, 1186632, 1195648, 1205648, 1212064
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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58472 is a term because;
58472 = 86^2 + 226^2.
58473 = 48^2 + 237^2 = 147^2 + 192^2.
58474 = 57^2 + 235^2 = 125^2 + 207^2 = 143^2 + 195^2.
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MAPLE
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N:= 10^6: # get all terms <= N-2
R:= Vector(N):
for x from 1 to floor(sqrt(N)) do
for y from 1 to min(x, floor(sqrt(N-x^2))) do
R[x^2+y^2]:= R[x^2+y^2]+1
od od:
count:= 0:
for n from 1 to N-2 do
if [R[n], R[n+1], R[n+2]] = [1, 2, 3] then
count:= count+1; A[count]:= n;
fi
od:
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PROG
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(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; }
isok(n) = is(n, 1) && is(n+1, 2) && is(n+2, 3);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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