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A279399 Irregular triangle read by rows. Row n gives the primes of the smallest positive restricted residue system modulo A033949(n). 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A238205 A186702 A141710 * A321784 A225889 A070647
KEYWORD
nonn,tabf
AUTHOR
Wolfdieter Lang, Jan 25 2017
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)