

A335865


Moduli a(n) = v(n) for the simple difference sets of Singer type of order m(n) (v(n), m(n)+1, 1) in the additive group modulo v(n) = m(n)^2 + m(n) + 1, with m(n) = A000961(n).


5



3, 7, 13, 21, 31, 57, 73, 91, 133, 183, 273, 307, 381, 553, 651, 757, 871, 993, 1057, 1407, 1723, 1893, 2257, 2451, 2863, 3541, 3783, 4161, 4557, 5113, 5403, 6321, 6643, 6973, 8011, 9507, 10303, 10713, 11557, 11991, 12883, 14763, 15751
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OFFSET

1,1


COMMENTS

For details on these difference sets see A333852, with references, and a W. Lang link.
Because these simple difference sets of Singer type of order m = m(n) in the addive group (Z_{v(n)}, +) = RS(v(n)) = {0, 1, ..., v(n)1} are also simple symmetric balanced incomplete block designs (BIBD), the number of blocks b(n) is also v(n) = a(n). This is the number of simple difference sets of each of the A335865(n) classes.
Is a(n) = A138077(n1)?  R. J. Mathar, Sep 11 2020


LINKS

Table of n, a(n) for n=1..43.


FORMULA

a(n) = m(n)^2 + m(n) + 1 , with m(n) = A000961(n), for n >= 1.


EXAMPLE

n = 2, m(2) = 2, a(2) = 2^2 + 2 + 1 = 7. The simple Singer difference set of order 2 is denoted by (7, 3, 1) (Fano plane). There are two classes (A335866(2) = 2) obtained from the representative difference sets {0, 1, 3} and {0, 1, 5} by elementwise addition of 1, 2, ..., 6 taken modulo 7. Each class consists of 7 simple difference sets.


CROSSREFS

Cf. A000961, A333852, A335866, A138077.
Sequence in context: A011898 A098577 A004136 * A147409 A147342 A172310
Adjacent sequences: A335862 A335863 A335864 * A335866 A335867 A335868


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Jul 26 2020


STATUS

approved



