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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. 5
2, 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

1,1

COMMENTS

After 2880, 3360 has exactly the same density (5%).

LINKS

Table of n, a(n) for n=1..44.

Andreas Enge, William Hart, Fredrik Johansson, Short addition sequences for theta functions, arXiv:1608.06810 [math.NT], (24-August-2016)

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%.

PROG

(PARI) r=0; 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))

print1(2); r=1; for(n=2, 1e6, t=sq(n)/n; if(t<r, r=t; print1(", "n))) \\ Charles R Greathouse IV, Mar 30 2018

CROSSREFS

Cf. A084848.

Sequence in context: A062923 A133464 A273731 * A013914 A228718 A222123

Adjacent sequences:  A085632 A085633 A085634 * A085636 A085637 A085638

KEYWORD

nonn

AUTHOR

Jose R. Brox (tautocrona(AT)terra.es), Jul 10 2003

EXTENSIONS

More terms from Jud McCranie, Jul 12 2003

STATUS

approved

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Last modified April 24 04:19 EDT 2018. Contains 302984 sequences. (Running on oeis4.)