A060940 Triangle in which n-th row gives the phi(n) terms appearing as initial primes in arithmetic progressions with difference n, with initial term equal to the smallest positive residue coprimes to n.

2, 3, 7, 5, 5, 7, 11, 7, 13, 19, 7, 11, 29, 23, 17, 11, 19, 13, 17, 11, 13, 23, 19, 11, 13, 23, 43, 17, 11, 13, 17, 19, 23, 13, 47, 37, 71, 17, 29, 19, 31, 43, 13, 17, 19, 23, 53, 41, 29, 17, 31, 19, 59, 47, 61, 23, 37, 103, 29, 17, 19, 23, 53, 41, 31, 17, 19, 37, 23, 41, 43, 29

Offset: 1

Author

Labos Elemer, May 07 2001

Keywords

• nonn
• tabf

Examples

			For differences 1, 2, 3, 4, 5, 6, 7, .. the initial primes are 2; 3; 7, 5; 5, 7; 11, 7, 13, 19; 7, 11; 29, 23, 17, 11, 19, 13; ... etc. Suitable initial values (coprimes to difference) are in A038566. Position of end(start) of rows is given by values of A002088.
From _Seiichi Manyama_, Apr 02 2018: (Start)
   n | phi(n)|
  ---+-------+------------------------
   1 |   1   |  2;
   2 |   1   |  3;
   3 |   2   |  7,  5;
   4 |   2   |  5,  7;
   5 |   4   | 11,  7, 13, 19;
   6 |   2   |  7, 11;
   7 |   6   | 29, 23, 17, 11, 19, 13;
   8 |   4   | 17, 11, 13, 23;
   9 |   6   | 19, 11, 13, 23, 43, 17;
  10 |   4   | 11, 13, 17, 19;         (End)
		

Links

• Seiichi Manyama, Rows n = 1..200, flattened
• Eric Weisstein's MathWorld, Dirichlet's theorem
• Wikipedia, Dirichlet's theorem on arithmetic progressions

Crossrefs

Cf. A000010 (phi), A002088, A038566, A034693, A034694, A002144, A007519, A088732, etc..