

A143253


Irregular triangle by rows, squares mod primes; 1<=k<=n.


0



1, 1, 1, 1, 4, 4, 1, 1, 4, 2, 2, 4, 1, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 1, 4, 9, 16, 6, 17, 11, 7, 5, 5, 7, 11, 17, 6, 16, 9, 4, 1, 1, 4, 9, 16, 2, 13, 3, 18, 12, 8, 6, 6, 8, 12, 18, 3, 13, 2, 16, 9, 4, 1
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OFFSET

1,5


LINKS

Table of n, a(n) for n=1..91.
Wikipedia, Quadratic reciprocity.


FORMULA

Triangle read by rows nth row = the first p(n)  1 terms of k^2 mod p(n) such that the next term 0 = and the cycle repeats. The 0 term and repeating cycle are not included in the triangle. 1<=k<=n.


EXAMPLE

First few rows of the triangle =
1;
1, 1
1, 4, 4, 1;
1, 4, 2, 2, 4, 1;
1, 4, 9, 5, 3, 3, 5, 9, 4, 1;
1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1;
...
Row 3 = (1, 4, 4, 1) = the truncated cycle of (1, 4, 4, 1, 0, 1, 4, 4, 1, 0,...) = squares of (1, 2, 3,...) mod 5


MATHEMATICA

Table[ Mod[k^2, Prime@n], {n, 10}, {k, Prime@n  1}] // Flatten (* Robert G. Wilson v, Aug 31 2008 *)


CROSSREFS

Cf. A000040.
Sequence in context: A214499 A234002 A016496 * A060036 A202024 A319703
Adjacent sequences: A143250 A143251 A143252 * A143254 A143255 A143256


KEYWORD

nonn,tabf


AUTHOR

Gary W. Adamson, Aug 02 2008


STATUS

approved



