A279399 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..105.

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).

EXAMPLE

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.

Sequence in context: A238205 A186702 A141710 * A321784 A376833 A225889

Adjacent sequences: A279396 A279397 A279398 * A279400 A279401 A279402

KEYWORD

nonn,tabf

AUTHOR

Wolfdieter Lang, Jan 25 2017

STATUS

approved