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A254309
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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.
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3
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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
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1,2
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COMMENTS
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Each row is a complete set of incongruent primitive roots.
Each row is a permutation of the corresponding row in A060749.
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LINKS
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EXAMPLE
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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).
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MAPLE
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with(numtheory):
T:= n-> (p-> seq(primroot(p)&^k mod p, k=select(
h-> igcd(h, p-1)=1, [$1..p-1])))(ithprime(n)):
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MATHEMATICA
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Table[nn = p; Table[Mod[PrimitiveRoot[nn]^k, nn], {k, Select[Range[nn - 1], CoprimeQ[#, nn - 1] &]}], {p, Prime[Range[12]]}] // Grid
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CROSSREFS
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Last elements of rows give A255367.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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