A001132 -id:A001132 - cp's OEIS frontend

A002334 Least positive integer x such that prime A038873(n) = x^2 - 2y^2 for some y.

2, 3, 5, 5, 7, 7, 7, 11, 9, 9, 11, 13, 11, 11, 15, 13, 13, 13, 17, 15, 19, 15, 19, 17, 21, 17, 19, 17, 17, 19, 21, 25, 19, 19, 23, 25, 23, 21, 23, 21, 21, 29, 23, 25, 23, 27, 29, 23, 31, 33, 25, 29, 27, 25, 25, 27, 29, 35, 31, 31, 27, 29, 33, 31, 29, 29, 29, 29, 37, 31, 41, 35

Offset: 1

N. J. A. Sloane

A prime p is representable in the form x^2 - 2y^2 iff p is 2 or p == 1 or 7 (mod 8). - Pab Ter (pabrlos2(AT)yahoo.com), Oct 22 2005
From Wolfdieter Lang, Feb 17 2015: (Start)
For the corresponding y terms see A002335.
a(n), together with A002335(n), gives the fundamental positive  solution of the first class of this (generalized) Pell equation. The prime 2 has only one class of proper solutions. The fundamental positive solutions of the second class for the primes from A001132 are given in A254930 and A254931. (End)

			The first solutions [x(n), y(n)] are (the prime is given as first entry): [2,[2,1]], [7,[3,1]], [17,[5,2]], [23,[5,1]], [31,[7,3]], [41,[7,2]], [47,[7,1]], [71,[11,5]], [73,[9,2]], [79,[9,1]], [89,[11,4]], [97,[13,6]], [103,[11,3]], [113,[11,2]], [127,[15,7]], [137,[13,4]], [151,[13,3]], [167,[13,1]], [191,[17,7]], [193,[15,4]], [199,[19,9]], [223,[15,1]], [233,[19,8]], [239,[17,5]], [241,[21,10]], [257,[17,4]], [263,[19,7]], [271,[17,3]], ... - _Wolfdieter Lang_, Feb 17 2015

A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Robert Israel, Table of n, a(n) for n = 1..10000
A. J. C. Cunningham, Quadratic Partitions, Hodgson, London, 1904 [Annotated scans of selected pages]

Cf. A002335, A035251.

with(numtheory): readlib(issqr): for i from 1 to 250 do p:=ithprime(i): pmod8:=modp(p,8): if p=2 or pmod8=1 or pmod8=7 then for y from 1 do x2:=p+2*y^2: if issqr(x2) then printf("%d,",sqrt(x2)): break fi od fi od: # Pab Ter, May 08 2004

maxPrimePi = 200;
Reap[Do[If[MatchQ[Mod[p, 8], 1|2|7], rp = Reduce[x > 0 && y > 0 && p == x^2 - 2*y^2, {x, y}, Integers]; If[rp =!= False, xy = {x, y} /. {ToRules[rp /. C[1] -> 1]}; x0 = xy[[All, 1]] // Min // Simplify; Print[{p, xy[[1]]} ]; Sow[x0]]], {p, Prime[Range[maxPrimePi]]}]][[2, 1]] (* Jean-François Alcover, Oct 27 2019 *)

a(n)^2 - 2*A002335(n)^2 = A038873(n), n >= 1, and a(n) is the least positive integer satisfying this Pell type equation. - Wolfdieter Lang, Feb 12 2015

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004

The name has been changed in order to be more precise and to conform with A002335. The offset has been changed to 1. - Wolfdieter Lang, Feb 12 2015

A042999 Primes congruent to {2, 3, 5} (mod 8).

Original entry on oeis.org

2, 3, 5, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 131, 139, 149, 157, 163, 173, 179, 181, 197, 211, 227, 229, 251, 269, 277, 283, 293, 307, 317, 331, 347, 349, 373, 379, 389, 397, 419, 421, 443

Offset: 1

N. J. A. Sloane

Apart from the initial term the same as A003629. - R. J. Mathar, May 23 2008

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms Vincenzo Librandi)

Cf. A001132 (complement).

[p: p in PrimesUpTo(500) | p mod 8 in [2, 3, 5]]; // Vincenzo Librandi, Aug 08 2012

Select[Prime[Range[300]],MemberQ[{2,3,5},Mod[#,8]]&] (* Vincenzo Librandi, Aug 08 2012 *)

A049596 Primes p such that x^9 = 2 has a solution mod p.

Original entry on oeis.org

2, 3, 5, 11, 17, 23, 29, 31, 41, 43, 47, 53, 59, 71, 83, 89, 101, 107, 113, 127, 131, 137, 149, 157, 167, 173, 179, 191, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 281, 283, 293, 311, 317, 347, 353, 359, 383, 389, 397, 401, 419, 431, 439, 443, 449

Offset: 1

N. J. A. Sloane

Coincides with sequence of "primes p such that x^27 = 2 has a solution mod p" for first 339 terms, then diverges.

Complement of A059262 relative to A000040. - Vincenzo Librandi, Sep 15 2012

			0^9 == 2 (mod 2). 2^9 == 2 (mod 3). 2^9 == 2 (mod 5). 6^9 == 2 (mod 11). 2^9 == 2 (mod 17). 9^9 == 2 (mod 23). 11^9 == 2 (mod 29). 16^9 == 2 (mod 31). 20^9 == 2 (mod 41). 26^9 == 2 (mod 43). - _R. J. Mathar_, Jul 20 2025

R. J. Mathar, Table of n, a(n) for n = 1..1000
Index entries for related sequences

Cf. A000040, A001132, A059262.

[p: p in PrimesUpTo(500) | exists(t){x : x in ResidueClassRing(p) | x^9 eq 2}]; // Vincenzo Librandi, Sep 15 2012

ok[p_]:= Reduce[Mod[x^9 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

A115586 Prime moduli p for which 2 is neither a quadratic residue nor a primitive root.

Original entry on oeis.org

43, 109, 157, 229, 251, 277, 283, 307, 331, 397, 499, 571, 643, 683, 691, 733, 739, 811, 971, 997, 1013, 1021, 1051, 1069, 1093, 1163, 1181, 1429, 1459, 1579, 1597, 1613, 1627, 1699, 1709, 1723, 1789, 1811, 1933, 2003, 2011, 2179, 2203, 2251

Offset: 1

Don Reble, Mar 11 2006

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001122, A001132, A001133, A003629.

Intersection of A216838 and A003629.

select(p -> isprime(p) and numtheory:-order(2,p) <> p-1, [seq(seq(8*i+j,j=[3,5]),i=1..1000)]); # Robert Israel, Apr 02 2018

Select[Prime[Range[400]], MultiplicativeOrder[2, #] != # - 1 && JacobiSymbol[2, #] == -1 &] (* Alonso del Arte, Jun 08 2014 *)

is(n)=n>2&&isprime(n)&&kronecker(2,n)!=1&&znprimroot(n)!=2 \\ Lear Young, Mar 26 2014

A230077 Table a(n,m) giving in row n all k from {1, 2, ..., prime(n)-1} for which the Legendre symbol (k/prime(n)) = +1, for odd prime(n).

Original entry on oeis.org

1, 1, 4, 1, 4, 2, 1, 4, 9, 5, 3, 1, 4, 9, 3, 12, 10, 1, 4, 9, 16, 8, 2, 15, 13, 1, 4, 9, 16, 6, 17, 11, 7, 5, 1, 4, 9, 16, 2, 13, 3, 18, 12, 8, 6, 1, 4, 9, 16, 25, 7, 20, 6, 23, 13, 5, 28, 24, 22, 1, 4, 9, 16, 25, 5, 18, 2, 19, 7, 28, 20, 14, 10, 8

Offset: 2

Wolfdieter Lang, Oct 25 2013

The length of row n is r(n) = (prime(n) - 1)/2, with prime(n) = A000040(n), n >= 2.
If k from {1, 2, ..., p-1} appears in row n then the Legendre symbol (k/prime(n)) = +1 otherwise it is -1.
The Legendre symbol (k/p), p an odd prime and gcd(k,p) = 1, is +1 if there exists an integer x with x^2 == k (mod p) and -1 otherwise. It is sufficient to consider k from {1, 2, ..., p-1} (gcd(0,p) = p, not 1) because (k/p) = ((k + l*p)/p) for integer l. Because (p - x)^2 == x^2 (mod p), it is also sufficient to consider only x^2 from {1^2, 2^2, ..., ((p-1)/2)^2} which are pairwise incongruent modulo p. See the Hardy-Wright reference. p. 68-69.
For odd primes p one has for the Legendre symbol ((p-1)/p) =  (-1/p) = (-1)^(r(n)) (see above for the row length r(n), and theorem 82, p. 69 of Hardy-Wright), and this is +1 for prime p == 1 (mod 4) and -1 for p == 3 (mod 4). Therefore k = p-1 appears in row n iff p = prime(n) is from A002144 = 5, 13, 17, 29, 37, 41,...
For n>=4 (prime(n)>=7) at least one of the integers 2, 3, or 6 appears in every row. - Geoffrey Critzer, May 01 2015

			The irregular table a(n,m) begins (here p(n)=prime(n)):
n, p(n)\m 1 2 3  4  5  6   7   8   9  10  11  12  13  14  15
2,   3:   1
3,   5:   1 4
4,   7:   1 4 2
5,  11:   1 4 9  5  3
6,  13:   1 4 9  3 12 10
7,  17:   1 4 9 16  8  2  15  13
8,  19:   1 4 9 16  6 17  11   7   5
9,  23:   1 4 9 16  2 13   3  18  12   8   6
10, 29:   1 4 9 16 25  7  20   6  23  13   5  28  24  22
11, 31    1 4 9 16 25  5  18   2  19   7  28  20  14  10   8
...
Row n=12, p(n)=37: 1, 4, 9, 16, 25, 36, 12, 27, 7, 26, 10, 33, 21, 11, 3, 34, 30, 28.
Row n=13, p(n)=41: 1, 4, 9, 16, 25, 36, 8, 23, 40, 18, 39, 21, 5, 32, 20, 10, 2, 37, 33, 31.
(2/p) = +1 for n=4, p(4) = 7; p(7) = 17, p(9) = 23, p(11) = 31, p(13) = 41, ... This leads to A001132 (primes 1 or 7 (mod 8)).
4 = 5 - 1 appears in row n=3 for p(3)=5 because 5 is from A002144. 10 cannot appear in row 5 for p(5)=11 because 11 == 3 (mod 4), hence 11 is not in A002144.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. Fifth ed., Clarendon Press, 2003.

Alois P. Heinz, Rows n = 2..100, flattened

Cf. A000040, A002144, A063987.

T:= n-> (p-> seq(irem(m^2, p), m=1..(p-1)/2))(ithprime(n)):
seq(T(n), n=2..12);  # Alois P. Heinz, May 07 2015

Table[Table[Mod[a^2, p], {a, 1, (p - 1)/2}], {p,
Prime[Range[2, 20]]}] // Grid (* Geoffrey Critzer, Apr 30 2015 *)

a(n,m) = m^2 (mod prime(n)), n >= 2, where prime(n) = A000040(n), m = 1, 2, ..., (prime(n) - 1)/2.

A296937 Rational primes that decompose in the field Q(sqrt(13)).

Original entry on oeis.org

3, 17, 23, 29, 43, 53, 61, 79, 101, 103, 107, 113, 127, 131, 139, 157, 173, 179, 181, 191, 199, 211, 233, 251, 257, 263, 269, 277, 283, 311, 313, 337, 347, 367, 373, 389, 419, 433, 439, 443, 467, 491, 503, 521, 523, 547, 563, 569, 571, 599, 601, 607, 641

Offset: 1

N. J. A. Sloane, Dec 26 2017

Is this the same sequence as A141188 or A038883? - R. J. Mathar, Jan 02 2018
From Jianing Song, Apr 21 2022: (Start)
Primes p such that Kronecker(13, p) = Kronecker(p, 13) = 1, where Kronecker() is the Kronecker symbol. That is to say, primes p that are quadratic residues modulo 13.
Primes p such that p^6 == 1 (mod 13).
Primes p == 1, 3, 4, 9, 10, 12 (mod 13). (End)

Cf. A011583 (kronecker symbol modulo 13), A038883.
Rational primes that decompose in the quadratic field with discriminant D: A139513 (D=-20), A191019 (D=-19), A191018 (D=-15), A296920 (D=-11), A033200 (D=-8), A045386 (D=-7), A002144 (D=-4), A002476 (D=-3), A045468 (D=5), A001132 (D=8), A097933 (D=12), this sequence (D=13), A296938 (D=17).
Cf. A038884 (inert rational primes in the field Q(sqrt(13))).

Load the Maple program HH given in A296920. Then run HH(13, 200); This produces A296937, A038884, A038883.

isA296937(p) = isprime(p) && kronecker(p,13) == 1 \\ Jianing Song, Apr 21 2022

Equals A038883 \ {13}. - Jianing Song, Apr 21 2022

A091069 Moebius mu sequence for real quadratic extension sqrt(2).

Original entry on oeis.org

1, 0, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 0, -1, 0

Offset: 1

Marc LeBrun, Dec 17 2003

Analog of Moebius mu with sqrt(2) adjoined. Same as mu (A008683) except: 0 for even n (A005843) due to square (extended prime) factor (sqrt(2))^2 and rational primes of the form 8k+/-1 (A001132) factor into conjugate (extended prime) pairs (a + b*sqrt(2))(a - b*sqrt(2)), thus contributing +1 to the product instead of -1; e.g., 7 = (3 + sqrt(2))(3 - sqrt(2)).

For even n a(n) must be 0 because 2 is a square in the quadratic field and so the mu-analog is 0. Of course this coincidentally matches the 0's at even n in A087003. For odd n, from its definition as a product, |a(n)| MUST be the same as that of |mu(n)|. Since from the above we know that A087003(n) is the same as mu(n) at odd n, we can conclude that |a(n)| = |A087003(n)| for all n.

			a(21) = (-1)*(+1) = -1 because 21 = 3*7 where 3 and 7 are congruent to +3 and -1 mod 8 respectively.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Theorem 256, p. 221.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Absolute values are the same as those of A087003.
Cf. A008683 (original Moebius function over the integers), A318608 (Moebius function over Z[sqrt(i)], also having the same absolute value as a(n)).
Cf. A001132, A005843, A091337.

a(n)=
{
    my(r=1, f=factor(n));
    for(j=1, #f[, 1], my(p=f[j, 1], e=f[j, 2]);
        if(p==2||e>=2, r=0);
        if((Mod(p,8)==3||Mod(p,8)==5)&e==1, r*=-1);
    );
    return(r);
} \\ Jianing Song, Aug 30 2018

a(n) = 0 if n even or has a square prime factor, otherwise Product_{p divides n} (2 - |p mod 8|) where the product is taken over the primes.
From Jianing Song, Aug 30 2018: (Start)
Multiplicative with a(p^e) = 0 if p = 2 or e > 1, a(p) = 1 if p == +-1 (mod 8) and -1 if p == +-3 (mod 8).
For squarefree n, a(n) = Kronecker symbol (n, 2) (or (2, n)) = A091337(n). Also for these n, a(n) = A318608(n) if n even or n == 1 (mod 8), otherwise -A318608(n).
(End)

A258149 Triangle of the absolute difference of the two legs (catheti) of primitive Pythagorean triangles.

Original entry on oeis.org

1, 0, 7, 7, 0, 17, 0, 1, 0, 31, 23, 0, 0, 0, 49, 0, 17, 0, 23, 0, 71, 47, 0, 7, 0, 41, 0, 97, 0, 41, 0, 7, 0, 0, 0, 127, 79, 0, 31, 0, 0, 0, 89, 0, 161, 0, 73, 0, 17, 0, 47, 0, 119, 0, 199, 119, 0, 0, 0, 1, 0, 73, 0, 0, 0, 241

Offset: 2

Wolfdieter Lang, Jun 10 2015

For primitive Pythagorean triangles characterized by certain (n,m) pairs and references see A225949.
Here a(n,m) = 0 for non-primitive Pythagorean triangles, and for primitive Pythagorean triangles a(n,m) = abs(n^2 - m^2 - 2*n*m) = abs((n-m)^2 - 2*m^2).
The number of non-vanishing entries in row n is A055034(n).
D(n,m):= n^2 - m^2 - 2*n*m >= 0 if 1 <= m <= floor(n/(sqrt(2)+1)), and D(n,m) < 0 if n/(sqrt(2)+1)+1 <= m <= n-1, for n >= 2.
The Pell equation (n-m)^2 - 2*m^2 = +/- N is important here to find the representations of +N or -N in the triangle D(n,m). For instance, odd primes N have to be of the +1 (mod 8) (A007519) or -1 (mod 8) (A007522) form, that is, from A001132. See the Nagell reference, Theorem 110, p. 208 with Theorem 111, pp. 210-211. E.g., N = +7 appears for m = 1, 3, 9, 19, 53, ... (A077442) for n = 4, 8, 22, 46, 128, ... (2*A006452).
  N = -7 appears for n = 3, 9, 19, 53, 111, ... (A077442) and m = 2, 4, 8, 22, 46, ... (2*A006452).
For the  signed version 2*n*m - (n^2 - m^2) see A278717. - Wolfdieter Lang, Nov 30 2016

			The triangle a(n,m) begins:
n\m   1  2  3  4  5  6  7   8   9  10  11 ...
2:    1
3:    0  7
4:    7  0 17
5:    0  1  0 31
6:   23  0  0  0 49
7:    0 17  0 23  0 71
8:   47  0  7  0 41  0 97
9:    0 41  0  7  0  0  0 127
10:  79  0 31  0  0  0 89   0 161
11:   0 73  0 17  0 47  0 119   0 199
12: 119  0  0  0  1  0 73   0   0   0 241
...
a(2,1) = |1^2 - 2*1^2| = 1 for the primitive Pythagorean triangle (pPt) [3,4,5] with |3-4| = 1.
a(3,2) = |1^2 - 2*2^2| = 7 for the pPt [5,12,13] with |5 - 12| = 7.
a(4,1) = |3^2 - 2*1^2| = 7 for the pPt [15, 8, 17] with |15 - 8| = 7.

See also A225949.
T. Nagell, Introduction to Number Theory, Chelsea Publishing Company, New York, 1964, pp. 208, 210-211.

Cf. A249866, A222946, A225949, A222951, A258150, A278717 (signed).

a[n_, m_] /; n > m >= 1 && CoprimeQ[n, m] && (-1)^(n+m) == -1 := Abs[n^2 - m^2 - 2*n*m]; a[, ] = 0; Table[a[n, m], {n, 2, 12}, {m, 1, n-1}] // Flatten (* Jean-François Alcover, Jun 16 2015, after given formula *)

a(n,m) = abs(n^2 - m^2 -2*n*m) = abs((n-m)^2 - 2*m^2) if n > m >= 1, gcd(n,m) = 1, and n and m are integers of opposite parity (i.e., (-1)^(n+m) = -1); otherwise a(n,m) = 0.

A270951 Numbers k such that k | A000129(k-1).

Original entry on oeis.org

1, 7, 17, 23, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 169, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 367, 383, 385, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599, 601, 607, 617, 631, 641, 647, 673, 719, 727, 743

Offset: 1

Altug Alkan, Mar 26 2016

Although A246692 and this sequence have similar names, note that this sequence generates prime numbers most of the time.

Composite terms of this sequence are A351337.

			7 is a term because A000129(6) = 70 is divisible by 7.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000129, A001132, A246692, A270834, A351337 (composite terms).

Select[Range[1000], Divisible[Fibonacci[#-1, 2], #]&] (* Jean-François Alcover, Jun 06 2017 *)

a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
for(n=1, 1e3, if(Mod(a000129(n-1), n) == 0, print1(n, ", ")));

is(n)=(Mod([2,1;1,0],n)^(n-1))[2,1]==0 \\ Charles R Greathouse IV, Sep 11 2022

A296938 Rational primes that decompose in the field Q(sqrt(17)).

Original entry on oeis.org

2, 13, 19, 43, 47, 53, 59, 67, 83, 89, 101, 103, 127, 137, 149, 151, 157, 179, 191, 223, 229, 239, 251, 257, 263, 271, 281, 293, 307, 331, 349, 353, 359, 373, 383, 389, 409, 421, 433, 443, 457, 461, 463, 467, 491, 509, 523, 557, 563, 569, 577, 587, 593, 599

Offset: 1

N. J. A. Sloane, Dec 26 2017

From Jianing Song, Apr 21 2022: (Start)
Primes p such that kronecker(17, p) = kronecker(p, 17) = 1, where kronecker() is the kronecker symbol. That is to say, primes p that are quadratic residues modulo 17.
Primes p such that p^8 == 1 (mod 17).
Primes p == 1, 2, 4, 8, 9, 13, 15, 16 (mod 17). (End)

Cf. A011584 (kronecker symbol modulo 17).
Rational primes that decompose in the quadratic field with discriminant D: A139513 (D=-20), A191019 (D=-19), A191018 (D=-15), A296920 (D=-11), A033200 (D=-8), A045386 (D=-7), A002144 (D=-4), A002476 (D=-3), A045468 (D=5), A001132 (D=8), A097933 (D=12), A296937 (D=13), this sequence (D=17).
Cf. A038890 (inert rational primes in the field Q(sqrt(17))).

[p: p in PrimesUpTo(600) | KroneckerSymbol(p, 17) eq 1]; // Vincenzo Librandi, Apr 09 2020

Load the Maple program HH given in A296920. Then run HH(17, 200); This produces A296938, A038890, A038889.

Select[Prime[Range[200]], JacobiSymbol[#, 17]==1&] (* Vincenzo Librandi, Apr 09 2020 *)

isA296938(p) = isprime(p) && kronecker(p,17) == 1 \\ Jianing Song, Apr 21 2022

cp's OEIS Frontend

A002334 Least positive integer x such that prime A038873(n) = x^2 - 2y^2 for some y.

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A042999 Primes congruent to {2, 3, 5} (mod 8).

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Magma

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A049596 Primes p such that x^9 = 2 has a solution mod p.

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Magma

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A115586 Prime moduli p for which 2 is neither a quadratic residue nor a primitive root.

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A230077 Table a(n,m) giving in row n all k from {1, 2, ..., prime(n)-1} for which the Legendre symbol (k/prime(n)) = +1, for odd prime(n).

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A296937 Rational primes that decompose in the field Q(sqrt(13)).

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A091069 Moebius mu sequence for real quadratic extension sqrt(2).

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