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Search: id:A088195
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| A088195 |
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Distance (A088192) of primes from the largest quadratic residues modulo the primes (A088190), where the latter is non-monotonic. |
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+0
8
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| 3, 3, 3, 7, 3, 3, 3, 7, 3, 11, 7, 3, 7, 11, 3, 11, 7, 3, 3, 3, 3, 7, 17, 7, 3, 3, 3, 3, 3, 3, 13, 3, 11, 3, 7, 3, 11, 3, 3, 3, 3, 3, 13, 3, 11, 3, 3, 3, 3, 3, 11, 7, 11, 13, 3, 7, 7, 11, 7, 3, 3, 11, 19, 3, 11, 3, 3, 11, 17, 3, 11, 3, 7, 3, 13, 3, 3, 3, 3, 11, 11, 3, 3, 3, 3, 13, 19, 3, 3, 3, 7, 11
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The values are some odd primes, but never 5. The maximum value increases very slowly, it only reaches 31 for the first 20000 primes.
It is conjectured that if we denote the members of A088194 by D(n) and the member of this sequence by M(n) then if D(n)=-1 then M(n)=7, while if M(n)=3 then D(n)=0.
The values are odd primes, but never 5 (the primality is provable). The maximum value increases very slowly: it only reaches 43 for the first 10^5 primes.
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LINKS
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Ferenc Adorjan, The sequence of largest quadratic residues modulo the primes.
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PROGRAM
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(PARI) qrp_pm_nm(to)= {/* The distance of LQR from the primes where the sequence of the largest QR modulo the primes is non monotonic */ local(m, k=1, p, v=[]); for(i=2, to, m=1; p=prime(i); j=2; while((j<=(p-1)/2)&&(m<p-1), m=max(m, (j^2)%p); j++); if((m-k)<=0, v=concat(v, p-m)); k=m); print(v) }
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CROSSREFS
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Cf. A088190, A088191, A088192, A088193, A088194.
Sequence in context: A079988 A061021 A126608 this_sequence A131757 A135087 A084038
Adjacent sequences: A088192 A088193 A088194 this_sequence A088196 A088197 A088198
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KEYWORD
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easy,nonn
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AUTHOR
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Ferenc Adorjan (fadorjan(AT)freemail.hu), Sep 22 2003
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