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Search: id:A053200
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| A053200 |
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Pascal's triangle read by rows, where row n is read mod n. |
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+0
9
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| 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 3, 2, 3, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 4, 0, 6, 0, 4, 0, 1, 1, 0, 0, 3, 0, 0, 3, 0, 0, 1, 1, 0, 5, 0, 0, 2, 0, 0, 5, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 6, 4, 3, 0, 0, 0, 3, 4, 6, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list; table; graph; listen)
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OFFSET
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0,13
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COMMENT
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A number n is a prime if and only if (1+x)^n == 1+x^n (mod n), i.e. if and only if the n-th row is 1,0,0,...,0,1. This result underlies the proof of Agrawal, Kayal and Saxena that there is polynomial-time algorithm for primality testing. - njas, Feb 20, 2004
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REFERENCES
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M. Agrawal, N. Kayal and N. Saxena, PRIMES is in P, Ann. of Math. (2) 160 (2004), no. 2, 781-793.
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LINKS
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T. D. Noe, Rows n=0..100 of triangle, flattened
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EXAMPLE
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0; 0,0; 1,0,1; 1,0,0,1; 1,0,2,0,1; ...
Row 4 = 1 mod 4, 4 mod 4, 6 mod 4, 4 mod 4, 1 mod 4 = 1, 0, 2, 0, 1
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MAPLE
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f := n -> seriestolist( series( expand( (1+x)^n ) mod n, x, n+1)); (njas)
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CROSSREFS
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Row sums give A053204. Cf. A053201, A053202, A053203, A007318 (Pascal's triangle)
Cf. also A092241.
Sequence in context: A022902 A037273 A025426 this_sequence A140209 A050870 A103306
Adjacent sequences: A053197 A053198 A053199 this_sequence A053201 A053202 A053203
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KEYWORD
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nonn,nice,tabl
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AUTHOR
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Asher Auel (asher.auel(AT)reed.edu) Dec 12, 1999
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EXTENSIONS
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Corrected by T. D. Noe, Feb 08 2008
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