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 A085635 Compute S, the number of different quadratic residues modulo B for every base B. If the density S/B is smaller for B than for every B' less than B, then B is added to the sequence. 6
 1, 3, 4, 8, 12, 16, 32, 48, 80, 96, 112, 144, 240, 288, 336, 480, 560, 576, 720, 1008, 1440, 1680, 2016, 2640, 2880, 3600, 4032, 5040, 7920, 9360, 10080, 15840, 18480, 20160, 25200, 31680, 37440, 39600, 44352, 50400, 55440, 65520, 85680, 95760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS After 2880, 3360 has exactly the same density (5%). LINKS Keith F. Lynch, Table of n, a(n) for n = 1..200 (terms 1..111) from Hugo Pfoertner) Andreas Enge, William Hart, Fredrik Johansson, Short addition sequences for theta functions, arXiv:1608.06810 [math.NT], 2016-2018. EXAMPLE a(3)=4 because for B=4 the different quadratic residues are {0,1}, so S=2, the density is D_4=50%, that is smaller than D_2=100% and D_3=66.67%. MATHEMATICA Block[{s = Range[0, 2^14 + 1]^2, t}, t = Array[#/Length@ Union@ Mod[Take[s, # + 1], #] &, Length@ s - 1]; Map[FirstPosition[t, #][[1]] &, Union@ FoldList[Max, t]]] (* Michael De Vlieger, Sep 10 2018 *) PROG (PARI) r=-1; for(n=1, 1e6, t=1-sum(k=1, n, issquare(Mod(k, n)))/n; if(t>r, r=t; print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011 (PARI) sq1(m)=sum(n=0, m-1, issquare(Mod(n, m))) sq(n, f=factor(n))=prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(e>1, sq1(p^e), p\2+1)) r=2; for(n=1, 1e6, t=sq(n)/n; if(t

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Last modified August 18 13:09 EDT 2022. Contains 356212 sequences. (Running on oeis4.)