A297350 Start of record gaps between sums of two squares.
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
Offset: 1
Keywords
Examples
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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..43
Programs
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Mathematica
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 *) -
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])
Comments