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A297350 Start of record gaps between sums of two squares. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 28 18:20 EST 2023. Contains 359895 sequences. (Running on oeis4.)