0,13

Pascal's triangle read by rows, where row n is read mod n.

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. - N. J. A. Sloane (njas(AT)research.att.com), Feb 20, 2004

M. Agrawal, N. Kayal and N. Saxena, PRIMES is in P, Ann. of Math. (2) 160 (2004), no. 2, 781-793.

T. D. Noe, Rows n=0..100 of triangle, flattened

Row 4 = 1 mod 4, 4 mod 4, 6 mod 4, 4 mod 4, 1 mod 4 = 1, 0, 2, 0, 1

Triangle begins :

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 ;

f := n -> seriestolist( series( expand( (1+x)^n ) mod n, x, n+1)); (N. J. A. Sloane)

Row sums give A053204. Cf. A053201, A053202, A053203, A007318 (Pascal's triangle)

Cf. also A092241.

Cf. A007318.

Sequence in context: A037273 A158924 A025426 this_sequence A050870 A103306 A163510

Adjacent sequences: A053197 A053198 A053199 this_sequence A053201 A053202 A053203

nonn,tabl,nice

Asher Auel (asher.auel(AT)reed.edu) Dec 12, 1999

Corrected by T. D. Noe, Feb 08 2008

Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008 at the suggestion of R. J. Mathar