A279399 Irregular triangle read by rows. Row n gives the primes of the smallest positive restricted residue system modulo A033949(n).

3, 5, 7, 5, 7, 11, 2, 7, 11, 13, 3, 5, 7, 11, 13, 3, 7, 11, 13, 17, 19, 2, 5, 11, 13, 17, 19, 5, 7, 11, 13, 17, 19, 23, 3, 5, 11, 13, 17, 19, 23, 7, 11, 13, 17, 19, 23, 29, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 2, 5, 7, 13, 17, 19, 23, 29, 31, 2, 3, 11, 13, 17, 19, 23, 29, 31, 5, 7, 11, 13, 17, 19, 23, 29, 31, 2, 5, 7, 11, 17, 19, 23, 29, 31, 37, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37

Offset: 1

Author

Wolfdieter Lang, Jan 25 2017

Keywords

• nonn
• tabf

Comments

The length of row n is given by A279400(n)

For the restricted residue systems modulo n see A038566. For the primes of A038566 (for n >= 3) see A112484.

The primes of the restricted residue system modulo the (composite) positive numbers without a primitive root, given in A033949, are of interest for the determination of the Dirichlet characters modulo the A033949 numbers. For prime numbers (A000040) or for composite positive numbers that have prime primitive roots (A279398) the Dirichlet characters are determined from those of the prime primitive root.

Examples

			The triangle T(n, k) begins (here N = A033949(n)):
n,   N \ k 1  2  3  4  5  6  7  8  9 10 ...
1,   8:    3  5  7
2,  12:    5  7 11
3,  15:    2  7 11 13
4,  16:    3  5  7 11 13
5,  20:    3  7 11 13 17 19
6,  21:    2  5 11 13 17 19
7,  24:    5  7 11 13 17 19 23
8,  28:    3  5 11 13 17 19 23
9,  30:    7 11 13 17 19 23 29
10, 32:    3  5  7 11 13 17 19 23 29 31
11, 33:    2  5  7 13 17 19 23 29 31
12, 35:    2  3 11 13 17 19 23 29 31
13, 36:    5  7 11 13 17 19 23 29 31
14, 39:    2  5  7 11 17 19 23 29 31 37
15, 40:    3  7 11 13 17 19 23 29 31 37
...
		

Crossrefs

Cf. A000040, A033949, A038566, A112484, A279398, A279400, A279401.

Formula

Row n of T is given by the primes of row A033949(n) of A038566, for n >= 1.

T(n, k) = A112484(A033949(n), k), n >= 1, k = 1..A279400(n).