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

1,2

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..43

Example

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.

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 *)

Prog

(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])

Crossrefs

Cf. A001481, A022544, A357018.

Sequence in context: A271858 A189734 A221678 * A027041 A355866 A186767

Adjacent sequences: A297347 A297348 A297349 * A297351 A297352 A297353

Keyword

nonn

Author

Charles R Greathouse IV, Dec 28 2017

Status

approved