This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A053200 Binomial coefficients C(n,k) reduced modulo n, read by rows; T(0,0)=0 by convention. 13
 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; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS 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, Feb 20 2004 A020475 (n) = number of zeros in n-th row, for n > 0. - Reinhard Zumkeller, Jan 01 2013 REFERENCES M. Agrawal, N. Kayal and N. Saxena, PRIMES is in P, Ann. of Math. (2) 160 (2004), no. 2, 781-793. LINKS T. D. Noe, Rows n=0..100 of triangle, flattened EXAMPLE 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 ; MAPLE f := n -> seriestolist( series( expand( (1+x)^n ) mod n, x, n+1)); # N. J. A. Sloane MATHEMATICA Flatten[Join[{0}, Table[Mod[Binomial[n, Range[0, n]], n], {n, 20}]]] (* Harvey P. Dale, Apr 29 2013 *) PROG (Haskell) a053200 n k = a053200_tabl !! n !! k a053200_row n = a053200_tabl !! n a053200_tabl = [0] : zipWith (map . flip mod) [1..] (tail a007318_tabl) -- Reinhard Zumkeller, Jul 10 2015, Jan 01 2013 (PARI) T(n, k)=if(n, binomial(n, k)%n, 0) \\ Charles R Greathouse IV, Feb 07 2017 CROSSREFS Row sums give A053204. Cf. A053201, A053202, A053203, A007318 (Pascal's triangle). Cf. also A092241. Cf. A053214 (central terms, apart from initial 1). Sequence in context: A025426 A269244 A204246 * A050870 A103306 A269249 Adjacent sequences:  A053197 A053198 A053199 * A053201 A053202 A053203 KEYWORD nonn,tabl,nice AUTHOR Asher Auel (asher.auel(AT)reed.edu), Dec 12 1999 EXTENSIONS Corrected by T. D. Noe, Feb 08 2008 Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)