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Search: id:A060749
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| A060749 |
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Triangle in which n-th row lists all primitive roots modulo the n-th prime. |
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+0
16
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| 1, 2, 2, 3, 3, 5, 2, 6, 7, 8, 2, 6, 7, 11, 3, 5, 6, 7, 10, 11, 12, 14, 2, 3, 10, 13, 14, 15, 5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 2, 3, 8, 10, 11, 14, 15, 18, 19, 21, 26, 27, 3, 11, 12, 13, 17, 21, 22, 24, 2, 5, 13, 15, 17, 18, 19, 20, 22, 24, 32, 35, 6, 7, 11, 12, 13, 15, 17, 19, 22, 24
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of terms per row is given by A008330. For example, A008330(10) = 12 and the 12 primitive roots associated with prime number 29 are 2,3,8,10,11,14,15,18,19,21,26,27. - Alford Arnold (Alford1940(AT)aol.com), Aug 22 2004
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REFERENCES
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C. W. Curtis, Pioneers of Representation Theory ..., Amer. Math. Soc., 1999; see p. 3.
R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..9076 (first 100 rows)
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EXAMPLE
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Triangle begins:
1
2
2 3
3 5
2 6 7 8
2 6 7 11
3 5 6 7 10 11 12 14
2 3 10 13 14 15
5 7 10 11 14 15 17 19 20 21
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MATHEMATICA
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prQ[p_, a_] := Block[{d = Most@Divisors[p - 1]}, If[ GCD[p, a] == 1, FreeQ[ PowerMod[a, d, p], 1], False]]; f[n_] := Select[Range@n, prQ[n, # ] &]; Table[ f[Prime[n]], {n, 13}] // Flatten (from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 17 2005)
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PROGRAM
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{Haskell} main=print[[n|n<-[1..p-1], let h x=if x==1 then 1 else 1+h(x*n`mod`p)in h n==p-1]|p<-let p=2:[n|(n, r)<-drop 2(zip[1..](concat[replicate(2*n+1)(toInteger n)|n<-[1..]])), and[n`mod`x/=0|x<-takeWhile(<=r)p]]in p] (Stoeber)
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CROSSREFS
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Diagonals give A001918, A071894.
Cf. A008330, A046147.
Sequence in context: A018053 A067619 A113773 this_sequence A138305 A079375 A069933
Adjacent sequences: A060746 A060747 A060748 this_sequence A060750 A060751 A060752
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KEYWORD
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nonn,tabf,nice,easy
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AUTHOR
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njas, Apr 23 2001
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EXTENSIONS
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More terms from Alford Arnold (Alford1940(AT)aol.com), Aug 22 2004
More terms from Paul Stoeber (pstoeber(AT)uni-potsdam.de), Oct 08 2005
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