This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A063988 Triangle in which n-th row gives quadratic non-residues modulo the n-th prime. 2
 2, 2, 3, 3, 5, 6, 2, 6, 7, 8, 10, 2, 5, 6, 7, 8, 11, 3, 5, 6, 7, 10, 11, 12, 14, 2, 3, 8, 10, 12, 13, 14, 15, 18, 5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22, 2, 3, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 26, 27, 3, 6, 11, 12, 13, 15, 17, 21, 22, 23, 24, 26, 27, 29, 30, 2, 5, 6, 8, 13, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS T. D. Noe, Rows n=2..100 of triangle, flattened EXAMPLE Mod the 5th prime, 11, the quadratic residues are 1,3,4,5,9 and the non-residues are 2,6,7,8,10. 2; 2,3; 3,5,6; 2,6,7,8,10; ... MAPLE with(numtheory): for n from 1 to 20 do for j from 1 to ithprime(n)-1 do if legendre(j, ithprime(n)) = -1 then printf(`%d, `, j) fi; od: od: MATHEMATICA row[n_] := Select[p = Prime[n]; Range[p - 1], JacobiSymbol[#, p] == -1 &]; Table[row[n], {n, 2, 12}] // Flatten (* Jean-François Alcover, Oct 17 2012 *) PROG (PARI) residue(n, m)={local(r); r=0; for(i=0, floor(m/2), if(i^2%m==n, r=1)); r}   isA063988(n, m)=!residue(n, prime(m)) \\ Michael B. Porter, May 07 2010 (PARI) tabf(nn) = {for(n=1, prime(nn), p = prime(n); for (i=2, p-1, if (kronecker(i, p) == -1, print1(i, ", ")); ); print(); ); } \\ Michel Marcus, Jul 19 2013 (Python) from sympy import jacobi_symbol as J, prime def a(n):     p=prime(n)     return list(filter(lambda i: J(i, p)==-1, range(1, p))) for n in xrange(2, 13): print a(n) # Indranil Ghosh, May 27 2017 CROSSREFS Cf. A063987. Sequence in context: A166588 A277321 A262365 * A198453 A178932 A206439 Adjacent sequences:  A063985 A063986 A063987 * A063989 A063990 A063991 KEYWORD nonn,tabf,nice,easy AUTHOR Suggested by Gary W. Adamson, Sep 18 2001 EXTENSIONS More terms from James A. Sellers, Sep 25 2001 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 09:05 EST 2017. Contains 295957 sequences.