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A001917
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(p-1)/x, where p = prime(n) and x = ord(2,p), the smallest positive integer such that 2^x == 1 mod p.
(Formerly M0069 N0022)
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12
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1, 1, 2, 1, 1, 2, 1, 2, 1, 6, 1, 2, 3, 2, 1, 1, 1, 1, 2, 8, 2, 1, 8, 2, 1, 2, 1, 3, 4, 18, 1, 2, 1, 1, 10, 3, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 6, 1, 3, 8, 2, 10, 5, 16, 2, 1, 2, 3, 4, 3, 1, 3, 2, 2, 1, 11, 16, 1, 1, 4, 2, 2, 1, 1, 2, 1, 9, 2, 2, 1, 1, 10, 6, 6, 1, 2, 6, 1, 2, 1, 2, 2, 1, 3, 2, 1, 2, 1, 1, 1, 1, 1, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| Also number of cycles in permutations constructed from siteswap juggling pattern 1234...p.
Also A006694((p_n-1)/2) where p_n is the n-th odd prime. Conjecture: A006694(((p_n)^k-1)/2)=ka(n). - Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 26 2008
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REFERENCES
| I. Anderson and D. A. Preece, Combinatorially fruitful properies of ..., Discr. Math., 310 (2010), 312-324. - N. J. A. Sloane (njas(AT)research.att.com), Dec 24 2009
M. Kraitchik, Recherches sur la Th\'{e}orie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 131.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-10.
W. Meissner, Ueber die Teilbarkeit von 2^p-2 durch das Quadrat der Primzahl p = 1093, Sitzungsberichte K\"{o}niglich Preussischen Akadamie Wissenschaften Berlin, 35 (1913), 663-667.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 2..10000
V. Papadimitriou, The l_2^(p) and the ... ratio of the first hundred million primes [From Vassilis Papadimitriou (bpapa(AT)sch.gr), Mar 13 2010]
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MAPLE
| with(numtheory); [seq((ithprime(n)-1)/order(2, ithprime(n)), n=2..130)];
with(group); with(numtheory); gen_rss_perm := proc(n) local a, i; a := []; for i from 1 to n do a := [op(a), ((2*i) mod (n+1))]; od; RETURN(a); end; count_of_disjcyc_seq := [seq(nops(convert(gen_rss_perm(ithprime(j)-1), 'disjcyc')), j=2..)];
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MATHEMATICA
| a6694[n_] := Sum[ EulerPhi[d] / MultiplicativeOrder[2, d], {d, Divisors[2n + 1]}] - 1; a[n_] := a6694[(Prime[n]-1)/2]; Table[ a[n], {n, 2, 104}] (* From Jean-François Alcover, Dec 14 2011, after Vladimir Shevelev *)
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PROG
| (MAGMA) [ (p-1)/Modorder(2, p) where p is NthPrime(n): n in [2..100] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 09 2008]
(PARI) {for(n=2, 100, p=prime(n); print1((p-1)/znorder(Mod(2, p)), ", "))} [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 09 2008]
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CROSSREFS
| Cf. A006694 gives cycle counts of such permutations constructed for all odd numbers.
Cf. A001122, A115591, A001133, A001134, A001135, A001136, A101208
Sequence in context: A013632 A080121 A122901 * A091591 A109374 A079706
Adjacent sequences: A001914 A001915 A001916 * A001918 A001919 A001920
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Additional comments from Antti Karttunen, Jan 05 2000
More terms from N. J. A. Sloane (njas(AT)research.att.com), Dec 24 2009
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