cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A010398 Squares mod 37.

Original entry on oeis.org

0, 1, 3, 4, 7, 9, 10, 11, 12, 16, 21, 25, 26, 27, 28, 30, 33, 34, 36
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

A070459 sorted, dulicates removed. - R. J. Mathar, Jan 12 2024

Crossrefs

Cf. A010435, A028750.

Programs

  • Magma
    [n: n in [0..36] | IsSquare(R! n) where R:= ResidueClassRing(37)]; // Vincenzo Librandi Jan 31 2020
  • Mathematica
    Union[PowerMod[Range[37], 2, 37]] (* Vincenzo Librandi, Jan 31 2020 *)
  • Sage
    [quadratic_residues(37)] # Zerinvary Lajos, May 24 2009

A035267 Indices of nonzero terms in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m= 37.

Original entry on oeis.org

1, 3, 4, 7, 9, 11, 12, 16, 21, 25, 27, 28, 33, 36, 37, 41, 44, 47, 48, 49, 53, 63, 64, 67, 71, 73, 75, 77, 81, 83, 84, 99, 100, 101, 107, 108, 111, 112, 121, 123, 127, 132, 137, 139, 141, 144, 147, 148, 149, 151, 157, 159, 164, 169, 173, 175, 176, 181, 188
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Positive numbers represented by the indefinite quadratic form 3x^2+xy-3y^2, of discriminant 37. - N. J. A. Sloane, Jun 05 2014 [Typo corrected by Klaus Purath, Apr 24 2023]
Also positive numbers of the form x^2 + (2m+1)xy + (m^2+m-9)y^2, m, x, y integers. All squares as well as the products of any terms belong to the sequence. Thus, this set of terms is closed under multiplication. - Klaus Purath, Apr 24 2023
A positive integer k belongs to the sequence if and only if k (modulo 37) is a term of A010398 and, moreover, in the case that prime factors p of k are terms of A038914, they occur only with even exponents. Or, more briefly, any positive integer is a term of this sequence if none of its divisors is an odd power of primes from A038914. For these primes also p (modulo 37) = {2, 5, 6, 8, 13, ...} = A028750 applies. - Klaus Purath, May 12 2023

Links

Crossrefs

For primes see A141178.
Cf. A035219.

Programs

  • Mathematica
    Reap[For[n = 0, n <= 100, n++, If[ Reduce[ 3*x^2 + x*y - 3*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]] (* N. J. A. Sloane, Jun 05 2014 *)
  • PARI
    m=37; select(x -> x, direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)), 1) \\ Fixed by Andrey Zabolotskiy, Jul 30 2020

Extensions

More terms from Colin Barker, Jun 17 2014
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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