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A063987
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Triangle in which n-th row gives quadratic residues modulo the n-th prime.
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10
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1, 1, 1, 4, 1, 2, 4, 1, 3, 4, 5, 9, 1, 3, 4, 9, 10, 12, 1, 2, 4, 8, 9, 13, 15, 16, 1, 4, 5, 6, 7, 9, 11, 16, 17, 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28, 1, 2, 4, 5, 7, 8, 9, 10, 14, 16, 18, 19, 20, 25, 28, 1, 3, 4, 7, 9, 10, 11, 12, 16, 21, 25
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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LINKS
| T. D. Noe, Rows n=1..100 of triangle, flattened
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EXAMPLE
| Mod the 5-th prime, 11, the quadratic residues are 1,3,4,5,9 and the non-residues are 2,6,7,8,10.
1; 1; 1,4; 1,2,4; 1,3,4,5,9; ...
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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:
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MATHEMATICA
| row[n_] := (p = Prime[n]; Select[ Range[p - 1], JacobiSymbol[#, p] == 1 &]); Flatten[ Table[ row[n], {n, 1, 12}]] (* From Jean-François Alcover, Dec 21 2011 *)
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PROG
| (PARI) residue(n, m)={local(r); r=0; for(i=0, floor(m/2), if(i^2%m==n, r=1)); r}
isA063987(n, m)=residue(n, prime(m)) /* Michael B. Porter May 07 2010 */
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CROSSREFS
| Cf. A063988.
Sequence in context: A100353 A080508 A178141 * A010126 A021712 A014571
Adjacent sequences: A063984 A063985 A063986 * A063988 A063989 A063990
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KEYWORD
| nonn,tabf,nice,easy
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AUTHOR
| Suggested by Gary W. Adamson, Sep 18 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 25 2001
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