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A297350
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Start of record gaps between sums of two squares.
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2
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0, 2, 5, 20, 74, 90, 185, 377, 986, 1493, 5165, 16109, 16868, 31657, 52393, 101349, 105572, 241882, 284002, 685541, 1437353, 1751296, 1853866, 5588305, 9565544, 13305524, 20875482, 67070173, 135628357, 192085714, 264428585, 345869506, 426063725, 434120338, 672657850
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OFFSET
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1,2
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COMMENTS
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Numbers of the form A001481(i) such that the difference A001481(i+1)-A001481(i) reaches record values, where i is the index of a(n) in A001481. - Felix Fröhlich, Jan 09 2018
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..43
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EXAMPLE
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20 = 4^2 + 2^2 and 25 = 5^2 + 0^2 are both sums of two squares, but none of 21, 22, 23, or 24 are, and no previous gap is as long as 25 - 20 = 5.
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MATHEMATICA
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Block[{s = Select[Range[0, 10^6], SquaresR[2, #] != 0 &], t}, t = Differences@ s; s[[First@ FirstPosition[t, #] ]] & /@ Union@ FoldList[Max, t]] (* Michael De Vlieger, Jan 09 2018 *)
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PROG
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(PARI) is2(f)=for(i=if(f[1, 1]==2, 2, 1), #f~, if(bitand(f[i, 2], 1)==1 && bitand(f[i, 1], 3)==3, return(0))); 1
print1(r=0); last=2; forfactored(n=last+1, 10^9, if(!is2(n[2]), next); t=n[1]-last; if(t>r, r=t; print1(", "last)); last=n[1])
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CROSSREFS
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Cf. A001481, A022544, A357018.
Sequence in context: A271858 A189734 A221678 * A027041 A355866 A186767
Adjacent sequences: A297347 A297348 A297349 * A297351 A297352 A297353
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KEYWORD
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nonn
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AUTHOR
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Charles R Greathouse IV, Dec 28 2017
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STATUS
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approved
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