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.

Showing 1-3 of 3 results.

A259911 Triangular array; row k shows the discriminant of the field of the number having purely periodic continued fraction with period (j,k+1-j), for j=1..k.

Original entry on oeis.org

5, 12, 12, 21, 8, 21, 8, 60, 60, 8, 5, 24, 13, 24, 5, 60, 140, 12, 12, 140, 60, 77, 12, 285, 5, 285, 12, 77, 24, 28, 44, 120, 120, 44, 28, 24, 13, 5, 21, 168, 29, 168, 21, 5, 13, 140, 44, 168, 56, 1020, 1020, 56, 168, 44, 140, 165, 120, 93, 8, 1365, 40, 1365, 8, 93, 120, 165
Offset: 1

Views

Author

Clark Kimberling, Jul 20 2015

Keywords

Examples

			First eight rows:
  5
  12    12
  21     8    21
   8    60    60     8
   5    24    13    24     5
  60   140    12    12   140    60
  77    12   285     5   285    12    77
  24    28    44   120   120    44    28    24
The number whose continued fraction is periodic with period (1,1) is the golden ratio, (1+sqrt(5))/2, so that the number in row 1 is 5.
As a square array A(n,k) read by antidiagonals, where A(n,k) corresponds to the continued fraction with pure period (n,k):
   5,  12,  21,   8,    5,   60,   77,  24, ...
  12,   8,  60,  24,  140,   12,   28,   5, ...
  21,  60,  13,  12,  285,   44,   21, 168, ...
   8,  24,  12,   5,  120,  168,   56,   8, ...
   5, 140, 285, 120,   29, 1020, 1365, 440, ...
  60,  12,  44, 168, 1020,   40, 1932, 156, ...
  77,  28,  21,  56, 1365, 1932,   53, 840, ...
  24,   5, 168,   8,  440,  156,  840,  17, ...
  ...

Links

Crossrefs

Cf. A259912 (main diagonal of square array), A259913 (first column).

Programs

  • Mathematica
    v = Table[FromContinuedFraction[{j, {k + 1 - j, j}}], {k, 1, 20}, {j, 1, k}];
TableForm[NumberFieldDiscriminant[v]]

A259912 Discriminant of the field of the number having constant continued fraction [n,n,n,...].

Original entry on oeis.org

5, 8, 13, 5, 29, 40, 53, 17, 85, 104, 5, 37, 173, 8, 229, 65, 293, 328, 365, 101, 445, 488, 533, 145, 629, 680, 733, 197, 5, 904, 965, 257, 1093, 1160, 1229, 13, 1373, 1448, 61, 401, 1685, 1768, 1853, 485, 2029, 2120, 2213, 577, 2405, 2504, 2605, 677, 2813
Offset: 1

Views

Author

Clark Kimberling, Jul 20 2015

Keywords

Comments

Central numbers of the triangle at A259911.
It appears that a(n) = 5 for n in A002878 = (1,4,11,29,...), a bisection of the Lucas sequence.

Examples

			[3,3,3,...] = (1/2)(3 + sqrt(13)), so that a(3) = 13.

Links

Crossrefs

Cf. A259911, A259913.

Programs

  • Mathematica
    t = Table[FromContinuedFraction[{n, {n}}], {n, 1, 100}];
Flatten[NumberFieldDiscriminant[t]]

A259532 Triangular array: row k shows the discriminant of sqrt(j) + sqrt(k) for j=1..k.

Original entry on oeis.org

1, 8, 8, 12, 8, 12, 1, 2304, 2304, 1, 5, 8, 12, 8, 5, 24, 1600, 12, 12, 1600, 24, 28, 2304, 3600, 1, 3600, 2304, 28, 8, 12544, 2304, 5, 5, 2304, 12544, 8, 1, 8, 7056, 24, 5, 24, 7056, 8, 1, 40, 8, 2304, 28, 14400, 14400, 28, 2304, 8, 40, 44, 1600, 12, 8
Offset: 1

Views

Author

Clark Kimberling, Jul 20 2015

Keywords

Examples

			First seven rows:
1
8   8
12  8     12
1   2304  2304   1
5   8     12     8   5
24  1600  12     12  1600  24
28  2304  3600   1   3600  2304  28

Links

Crossrefs

Cf. A259911, A259912, A259913.

Programs

  • Mathematica
    t = Table[NumberFieldDiscriminant[Sqrt[j] + Sqrt[k + 1 - j]], {k, 1, 16}, {j, 1, k}]
TableForm[t] (* A259532 array *)
Flatten[t]   (* A259532 sequence *)
Showing 1-3 of 3 results.

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