|
Search: id:A001917
|
|
|
| A001917 |
|
(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)
|
|
+0
7
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
2,3
|
|
|
COMMENT
|
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
|
|
REFERENCES
|
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.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n = 2..10000
|
|
MAPLE
|
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..)];
|
|
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 this_sequence A091591 A109374 A079706
Adjacent sequences: A001914 A001915 A001916 this_sequence A001918 A001919 A001920
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
Additional comments from Antti Karttunen, Jan 05 2000
|
|
|
Search completed in 0.002 seconds
|
