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.

Previous Showing 31-33 of 33 results.

A035110 Numerators in expansion of a certain Dirichlet series.

Original entry on oeis.org

1, 6, 7, 11, 26, 26, 42, 42, 37, 62, 66, 66, 86, 156, 77, 51, 182, 122, 126, 106, 146, 252, 162, 182, 101, 182, 294, 286, 222, 206, 222, 372, 459, 396, 187, 266, 282, 286, 434, 302, 306, 462, 516, 171, 462, 676, 362, 462, 366, 386, 306, 402, 602, 1092, 426, 1092
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

The series is sum_{n>=1} a(n)/A031363(n)^(3s). [From R. J. Mathar, Jul 16 2010]

Links

  • M. Baake and R. V. Moody, Similarity submodules and semigroups in Quasicrystals and Discrete Geometry, ed. J. Patera, Fields Institute Monographs, vol. 10 AMS, Providence, RI (1998) pp. 1-13.

Extensions

More terms from R. J. Mathar, Jul 16 2010

A167415 Positive integers k such that there is no solution of the equation x^2 + y^2 + 3*x*y = 0 in Z/nZ except for the trivial one (0,0).

Original entry on oeis.org

2, 3, 6, 7, 13, 14, 17, 21, 23, 26, 34, 37, 39, 42, 43, 46, 47, 51, 53, 67, 69, 73, 74, 78, 83, 86, 91, 94, 97, 102, 103, 106, 107, 111, 113, 119, 127, 129, 134, 137, 138, 141, 146, 157, 159, 161, 163, 166, 167, 173, 182, 193, 194, 197, 201, 206, 214, 219
Offset: 1

Views

Author

Arnaud Vernier, Nov 03 2009

Keywords

Comments

Prime numbers of this sequence are congruent to {2,3} modulo 5.

Examples

			The only solution of the equation x^2 + y^2 + 3*x*y = 0 in Z/2Z is (0,0).
4 is not in the sequence because 0^2 + 2^2 + 3*2*0 = 4 == 0 (mod 4). 5 is not in the sequence because 1^2 + 1^2 + 3*1*1 = 5 == 0 (mod 5). 10 is not in the sequence because 2^2 + 2^2 + 3*2*2 = 20 == 0 (mod 10). - _R. J. Mathar_, Jun 16 2019

Crossrefs

Cf. A031363 (x^2 + y^2 + 3xy).

Programs

  • Maple
    isA167415 := proc(n)
    local x,y ;
    for x from 0 to n-1 do
        for y from x to n-1 do
            if modp(x^2+y^2+3*x*y,n) = 0 and (x <> 0 or y <> 0) then
                return false;
            end if;
        end do:
    end do:
    true ;
end proc:
for n from 2 to 300 do
    if isA167415(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jun 16 2019

Extensions

Name corrected by R. J. Mathar, Jun 16 2019 and Don Reble

A261522 Positive integers k such that x^2 - 23xy + y^2 + k = 0 has integer solutions.

Original entry on oeis.org

21, 41, 59, 75, 84, 89, 101, 111, 119, 125, 129, 131, 164, 189, 201, 236, 251, 269, 300, 311, 329, 336, 356, 369, 381, 404, 419, 425, 444, 461, 476, 479, 489, 500, 509, 516, 521, 524, 525, 531, 579, 581, 629, 656, 675, 719, 731, 756, 761, 801, 804, 831, 839
Offset: 1

Views

Author

Colin Barker, Aug 23 2015

Keywords

Examples

			41 is in the sequence because x^2 - 23xy + y^2 + 41 = 0 has integer solutions; for example, (x, y) = (2, 45).

Crossrefs

Cf. A004253, A237254.
Cf. A031363, A084917, A237351, A237599, A237606, A237609, A237610, A236330, A236331, A238240, A238245.
Previous Showing 31-33 of 33 results.

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

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