A279399 - OEIS

%I #12 Apr 02 2017 17:10:41

%S 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,

%T 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,

%U 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

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

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

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

%C 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.

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

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

%e The triangle T(n, k) begins (here N = A033949(n)):

%e n,   N \ k 1  2  3  4  5  6  7  8  9 10 ...

%e 1,   8:    3  5  7

%e 2,  12:    5  7 11

%e 3,  15:    2  7 11 13

%e 4,  16:    3  5  7 11 13

%e 5,  20:    3  7 11 13 17 19

%e 6,  21:    2  5 11 13 17 19

%e 7,  24:    5  7 11 13 17 19 23

%e 8,  28:    3  5 11 13 17 19 23

%e 9,  30:    7 11 13 17 19 23 29

%e 10, 32:    3  5  7 11 13 17 19 23 29 31

%e 11, 33:    2  5  7 13 17 19 23 29 31

%e 12, 35:    2  3 11 13 17 19 23 29 31

%e 13, 36:    5  7 11 13 17 19 23 29 31

%e 14, 39:    2  5  7 11 17 19 23 29 31 37

%e 15, 40:    3  7 11 13 17 19 23 29 31 37

%e ...

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

%K nonn,tabf

%O 1,1

%A _Wolfdieter Lang_, Jan 25 2017