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A254309 Irregular triangular array read by rows: T(n,k) is the least positive primitive root of the n-th prime p=prime(n) raised to successive powers of k (mod p) where 1<=k<=p-1 and gcd(k,p-1)=1.

%I A254309 #27 May 04 2015 14:48:28
%S A254309 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,
%T A254309 10,20,17,11,21,19,15,7,14,2,8,3,19,18,14,27,21,26,10,11,15,3,17,13,
%U A254309 24,22,12,11,21,2,32,17,13,15,18,35,5,20,24,22,19
%N A254309 Irregular triangular array read by rows: T(n,k) is the least positive primitive root of the n-th prime p=prime(n) raised to successive powers of k (mod p) where 1<=k<=p-1 and gcd(k,p-1)=1.
%C A254309 Each row is a complete set of incongruent primitive roots.
%C A254309 Each row is a permutation of the corresponding row in A060749.
%C A254309 Row lengths are A008330.
%C A254309 T(n,1) = A001918(n).
%H A254309 Alois P. Heinz, <a href="/A254309/b254309.txt">Rows n = 1..120, flattened</a>
%e A254309 1;
%e A254309 2;
%e A254309 2,  3;
%e A254309 3,  5;
%e A254309 2,  8,  7,  6;
%e A254309 2,  6, 11,  7;
%e A254309 3, 10,  5, 11, 14,  7, 12,  6;
%e A254309 2, 13, 14, 15,  3, 10;
%e A254309 5, 10, 20, 17, 11, 21, 19, 15,  7, 14;
%e A254309 2,  8,  3, 19, 18, 14, 27, 21, 26, 10, 11, 15;
%e A254309 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 13-1=12 are {1,5,7,11}. So we have: 2^1==2, 2^5==6, 2^7==11, and 2^11==7 (mod 13).
%p A254309 with(numtheory):
%p A254309 T:= n-> (p-> seq(primroot(p)&^k mod p, k=select(
%p A254309          h-> igcd(h, p-1)=1, [$1..p-1])))(ithprime(n)):
%p A254309 seq(T(n), n=1..15);  # _Alois P. Heinz_, May 03 2015
%t A254309 Table[nn = p;Table[Mod[PrimitiveRoot[nn]^k, nn], {k,Select[Range[nn - 1], CoprimeQ[#, nn - 1] &]}], {p,Prime[Range[12]]}] // Grid
%Y A254309 Cf. A001918, A008330, A060749.
%Y A254309 Last elements of rows give A255367.
%Y A254309 Row sums give A088144.
%K A254309 nonn,tabf
%O A254309 1,2
%A A254309 _Geoffrey Critzer_, May 03 2015