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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
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 (list; graph; refs; listen; history; text; internal format)
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 |   2   | 11,  7, 13, 19;

   6 |   4   |  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: A229794 A082734 A021425 * A318739 A205299 A222242

Adjacent sequences:  A060937 A060938 A060939 * A060941 A060942 A060943

KEYWORD

nonn,tabf

AUTHOR

Labos Elemer, May 07 2001

STATUS

approved

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Last modified April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)