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

1,1

Links

Seiichi Manyama, Rows n = 1..200, flattened

Eric Weisstein's MathWorld, Dirichlet's theorem

Wikipedia, Dirichlet's theorem on arithmetic progressions

Example

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)

Crossrefs

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

Sequence in context: A355278 A329412 A335292 * A318739 A205299 A222242

Adjacent sequences: A060937 A060938 A060939 * A060941 A060942 A060943

Keyword

nonn,tabf

Author

Labos Elemer, May 07 2001

Status

approved