The On-Line Encyclopedia of Integer Sequences (OEIS)

A329534 revision #47

A329534

Irregular triangle read by rows where row n > 1 lists the positive k <= n - 1 such that k == -k^2 (mod n).

1, 2, 3, 4, 2, 3, 5, 6, 7, 8, 4, 5, 9, 10, 3, 8, 11, 12, 6, 7, 13, 5, 9, 14, 15, 16, 8, 9, 17, 18, 4, 15, 19, 6, 14, 20, 10, 11, 21, 22, 8, 15, 23, 24, 12, 13, 25, 26, 7, 20, 27, 28, 5, 9, 14, 15, 20, 24, 29, 30, 31, 11, 21, 32, 16, 17, 33, 14, 20, 34, 8, 27, 35, 36, 18, 19, 37, 12, 26, 38

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

n-th row length gives A309307(n) = A000225(A001221(n)) = A034444(n) - 1.

A000961(n)-th row length is a nonprime number of the form 2^x - 1.

A024619(n)-th row length is Mersenne prime.

A006881(n)-th row length = 3.

n-th row sum gives (n-1)*A007875(n) = (n-1)*A000010(2^A001221(n)).

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

The irregular triangle T(n,k) begins

n\k 1 2 3 ...

2: 1

3: 2

4: 3

5: 4

6: 2 3 5

7: 6

8: 7

9: 8

10: 4 5 9

11: 9

12: 3 8 11

13: 12

14: 6 7 13

15: 5 9 14.

MATHEMATICA

Table[Select[Range@ n, Mod[n - #^2, n] == # &], {n, 39}] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

PROG

(MAGMA) [[k: k in [1..n-1] | -k^2 mod n eq k]: n in [1..38]];

(PARI) row(n) = select(x->(Mod(x, n) == -Mod(x, n)^2), [1..n-1]); \\ Michel Marcus, Nov 19 2019

CROSSREFS

Cf. A000010, A000225, A000688, A000961, A001221, A006881, A006530, A007875, A020639, A024619, A034444, A135972, A309307.

Sequence in context: A304113 A304112 A293446 * A360378 A256443 A046068

Adjacent sequences: A329531 A329532 A329533 * A329535 A329536 A329537

KEYWORD

nonn,tabf

AUTHOR

Juri-Stepan Gerasimov, Nov 15 2019

STATUS

editing