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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. 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 (list; graph; refs; listen; history; text; internal format)
 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 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). MAPLE with(numtheory): T:= n-> (p-> seq(primroot(p)&^k mod p, k=select(          h-> igcd(h, p-1)=1, [\$1..p-1])))(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

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Last modified August 7 09:16 EDT 2020. Contains 336274 sequences. (Running on oeis4.)