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A143253
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Irregular triangle by rows, squares mod primes; 1<=k<=n.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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REFERENCES
| Wikipedia (Quadratic reciprocity).
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FORMULA
| Triangle read by rows n-th 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.
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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
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MATHEMATICA
| Table[ Mod[k^2, Prime@n], {n, 10}, {k, Prime@n - 1}] // Flatten (* Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 31 2008 *)
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CROSSREFS
| Cf. A000040.
Sequence in context: A143484 A047214 A016496 * A060036 A202024 A166361
Adjacent sequences: A143250 A143251 A143252 * A143254 A143255 A143256
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KEYWORD
| nonn,tabf
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 02 2008
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