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A228179 Irregular table where the n-th row consists of the square roots of 1 in Z_n. 3
1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 3, 5, 7, 1, 8, 1, 9, 1, 10, 1, 5, 7, 11, 1, 12, 1, 13, 1, 4, 11, 14, 1, 7, 9, 15, 1, 16, 1, 17, 1, 18, 1, 9, 11, 19, 1, 8, 13, 20, 1, 21, 1, 22, 1, 5, 7, 11, 13, 17, 19, 23, 1, 24, 1, 25, 1, 26, 1, 13, 15, 27, 1, 28, 1, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

Each 1 starts a new row.

This is a subsequence of A020652.

Row n has A060594(n) entries.

Each row forms a subgroup of the multiplicative group of units of Z_n.

LINKS

Alois P. Heinz, Rows n = 2..2000 of irregular triangle, flattened

EXAMPLE

The table starts out as follows:

1

1 2

1 3

1 4

1 5

1 6

1 3 5 7

1 8

1 9

1 10

1 5 7 11

MAPLE

T:= n-> seq(`if`(k&^2 mod n=1, k, NULL), k=1..n-1):

seq(T(n), n=2..50);  # Alois P. Heinz, Aug 20 2013

MATHEMATICA

Flatten[Table[Position[Mod[Range[n]^2, n], 1], {n, 2, 50}]] (* T. D. Noe, Aug 20 2013 *)

PROG

(Sage) [[i for i in [1..k-1] if (i*i).mod(k)==1] for k in [2..n]] #changing n gives you the table up to the n-th row.

CROSSREFS

Cf. A060594, A038566, A020652, A082568.

Cf. A277776 (nontrivial square roots of 1).

Sequence in context: A077610 A329534 A317746 * A322313 A322315 A319338

Adjacent sequences:  A228176 A228177 A228178 * A228180 A228181 A228182

KEYWORD

nonn,easy,tabf

AUTHOR

Tom Edgar, Aug 20 2013

STATUS

approved

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)