Sequences

392,541 sequences

Number of symmetrically inequivalent coincidence rotations of index n in lattice Z^4.A031361
Number of symmetrically inequivalent coincidence rotations of index n in lattice Z^4.
Number of coincidence site modules of index 10n+1 with 10-fold symmetry in plane.A031362
Number of coincidence site modules of index 10n+1 with 10-fold symmetry in plane.
Positive numbers of the form x^2 + xy - y^2; or, of the form 5x^2 - y^2.A031363
Positive numbers of the form x^2 + xy - y^2; or, of the form 5x^2 - y^2.
Number of coincidence site modules of index 10n+1 in an icosahedral module.A031364
Number of coincidence site modules of index 10n+1 in an icosahedral module.
Expansion of a certain Dirichlet series.A031365
Expansion of a certain Dirichlet series.
Number of symmetrically inequivalent coincidence rotations of icosian ring of index n.A031366
Number of symmetrically inequivalent coincidence rotations of icosian ring of index n.
Inflation orbit counts.A031367
Inflation orbit counts.
Odd-indexed primes: a(n) = prime(2n-1).A031368
Odd-indexed primes: a(n) = prime(2n-1).
a(n) = prime(3n-1).A031369
a(n) = prime(3n-1).
a(n) = prime(4n-1).A031370
a(n) = prime(4n-1).
a(n) = prime(5n-1).A031371
a(n) = prime(5n-1).
a(n) = prime(6*n - 1).A031372
a(n) = prime(6*n - 1).
a(n) = prime(7n-1).A031373
a(n) = prime(7n-1).
a(n) = prime(8*n - 1).A031374
a(n) = prime(8*n - 1).
a(n) = prime(9n-1).A031375
a(n) = prime(9n-1).
a(n) = prime(10*n - 1).A031376
a(n) = prime(10*n - 1).
a(n) = prime(3n-2).A031377
a(n) = prime(3n-2).
a(n) = prime(4*n - 2).A031378
a(n) = prime(4*n - 2).
a(n) = prime(5*n - 2).A031379
a(n) = prime(5*n - 2).
a(n) = prime(6*n - 2).A031380
a(n) = prime(6*n - 2).
a(n) = prime(7*n - 2).A031381
a(n) = prime(7*n - 2).
a(n) = prime(8*n - 2).A031382
a(n) = prime(8*n - 2).
a(n) = prime(9*n - 2).A031383
a(n) = prime(9*n - 2).
a(n) = prime(10*n - 2).A031384
a(n) = prime(10*n - 2).
a(n) = prime(4*n-3).A031385
a(n) = prime(4*n-3).
a(n) = prime(5*n-3).A031386
a(n) = prime(5*n-3).
a(n) = prime(6*n-3).A031387
a(n) = prime(6*n-3).
a(n) = prime(7*n-3).A031388
a(n) = prime(7*n-3).
a(n) = prime(8*n-3).A031389
a(n) = prime(8*n-3).
a(n) = prime(9*n - 3).A031390
a(n) = prime(9*n - 3).
a(n) = prime(10*n-3).A031391
a(n) = prime(10*n-3).
a(n) = prime(5*n-4).A031392
a(n) = prime(5*n-4).
a(n) = prime(6*n - 4).A031393
a(n) = prime(6*n - 4).
a(n) = prime(7*n - 4).A031394
a(n) = prime(7*n - 4).
a(n) = prime(8*n - 4).A031395
a(n) = prime(8*n - 4).
Numbers k such that Pell equation x^2 - k*y^2 = -1 is soluble.A031396
Numbers k such that Pell equation x^2 - k*y^2 = -1 is soluble.
Nonsquarefree k such that Pell equation x^2 - k*y^2 = -1 is soluble.A031397
Nonsquarefree k such that Pell equation x^2 - k*y^2 = -1 is soluble.
Squarefree m with no 4k+3 factors such that Pell equation x^2 - m*y^2 = -1 is insoluble.A031398
Squarefree m with no 4k+3 factors such that Pell equation x^2 - m*y^2 = -1 is insoluble.
Numbers n with no 4k+3 factors such that the Pell equation x^2 - n y^2 = -1 is insoluble.A031399
Numbers n with no 4k+3 factors such that the Pell equation x^2 - n y^2 = -1 is insoluble.
Period of continued fraction for sqrt(k) equal for all a(n) <= k < a(n)+n.A031400
Period of continued fraction for sqrt(k) equal for all a(n) <= k < a(n)+n.
Period of continued fraction for sqrt(A031400(n)).A031401
Period of continued fraction for sqrt(A031400(n)).
Sum of terms in period of continued fraction for sqrt(a(n)) increases.A031402
Sum of terms in period of continued fraction for sqrt(a(n)) increases.
Sum of terms in period of continued fraction for sqrt(A031402(n)).A031403
Sum of terms in period of continued fraction for sqrt(A031402(n)).
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 1.A031404
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 1.
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 2.A031405
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 2.
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 3.A031406
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 3.
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 4.A031407
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 4.
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 5.A031408
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 5.
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 6.A031409
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 6.
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 7.A031410
Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 7.