

A254309


Irregular triangular array read by rows: T(n,k) is the least positive primitive root of the nth prime p=prime(n) raised to successive powers of k (mod p) where 1<=k<=p1 and gcd(k,p1)=1.


3



1, 2, 2, 3, 3, 5, 2, 8, 7, 6, 2, 6, 11, 7, 3, 10, 5, 11, 14, 7, 12, 6, 2, 13, 14, 15, 3, 10, 5, 10, 20, 17, 11, 21, 19, 15, 7, 14, 2, 8, 3, 19, 18, 14, 27, 21, 26, 10, 11, 15, 3, 17, 13, 24, 22, 12, 11, 21, 2, 32, 17, 13, 15, 18, 35, 5, 20, 24, 22, 19
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OFFSET

1,2


COMMENTS

Each row is a complete set of incongruent primitive roots.
Each row is a permutation of the corresponding row in A060749.
Row lengths are A008330.
T(n,1) = A001918(n).


LINKS

Alois P. Heinz, Rows n = 1..120, flattened


EXAMPLE

1;
2;
2, 3;
3, 5;
2, 8, 7, 6;
2, 6, 11, 7;
3, 10, 5, 11, 14, 7, 12, 6;
2, 13, 14, 15, 3, 10;
5, 10, 20, 17, 11, 21, 19, 15, 7, 14;
2, 8, 3, 19, 18, 14, 27, 21, 26, 10, 11, 15;
Row 6 contains 2,6,11,7 because 13 is the 6th prime number. 2 is the least positive primitive root of 13. The integers relatively prime to 131=12 are {1,5,7,11}. So we have: 2^1==2, 2^5==6, 2^7==11, and 2^11==7 (mod 13).


MAPLE

with(numtheory):
T:= n> (p> seq(primroot(p)&^k mod p, k=select(
h> igcd(h, p1)=1, [$1..p1])))(ithprime(n)):
seq(T(n), n=1..15); # Alois P. Heinz, May 03 2015


MATHEMATICA

Table[nn = p; Table[Mod[PrimitiveRoot[nn]^k, nn], {k, Select[Range[nn  1], CoprimeQ[#, nn  1] &]}], {p, Prime[Range[12]]}] // Grid


CROSSREFS

Cf. A001918, A008330, A060749.
Last elements of rows give A255367.
Row sums give A088144.
Sequence in context: A060749 A138305 A169897 * A079375 A069933 A204987
Adjacent sequences: A254306 A254307 A254308 * A254310 A254311 A254312


KEYWORD

nonn,tabf


AUTHOR

Geoffrey Critzer, May 03 2015


STATUS

approved



