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 1-10 of 19 results. Next

A110279 A floretion-generated sequence calculated using the same rules given for A108618 with initial seed x = + .5'i + .5'ii' + .5'ij' + .5'ik'; version: "tes".

Original entry on oeis.org

0, -1, -3, -5, -6, -5, -2, 0, 9, 8, 5, 3, -6, -9, -17, -13, -7, -4, 10, 8, 13, 13, 5, 1, -10, -14, -16, -13, -9, -3, 11, 12, 15, 11, 8, -7, -10, -16, -27, -10, -14, 5, 12, 14, 27, 12, 11, -9, -16, -22, -28, -11, -15, 9, 19, 17, 30, 12, 14, -8, -23, -25, -36, -20, -18, 6, 23, 29, 38, 24, 18, -8, -27, -37, -44, -32, -22, 6, 27, 41, 46
Offset: 0

Views

Author

Creighton Dement, Jul 18 2005

Keywords

Comments

The initial seed + .5'i + .5'ii' + .5'ij' + .5'ik' can be seen as an element of the space Q X C_3 where Q are the quaternions.
Floretion Algebra Multiplication Program, FAMP Code: 2tessumseq[ + .5'i + .5'ii' + .5'ij' + .5'ik']. SumType is set to: sum[Y[15]]

Links

Crossrefs

Cf. A108618, A110280, A110281, A110282.

A110281 A floretion-generated sequence calculated using the same rules given for A108618 with initial seed x = + .5'i + .5'ii' + .5'ij' + .5'ik'; version: "basei".

Original entry on oeis.org

0, -1, -1, -1, 0, 1, 2, 2, 1, 0, -5, -5, -6, -5, -1, 1, 7, 6, 6, 4, -3, -3, -9, -9, -8, -6, 0, 3, 7, 7, 7, 4, -3, -5, -10, -9, -10, -2, -1, 6, 12, 7, 12, 0, -1, -8, -15, -11, -14, -2, 0, 9, 13, 9, 13, -1, -4, -10, -18, -12, -17, -3, 2, 10, 18, 14, 17, 3, -4, -14, -22, -20, -21, -7, 2, 14, 22, 22, 21, 7, -4, -18, -26, -28, -25, -11, 2, 18
Offset: 0

Views

Author

Creighton Dement, Jul 18 2005

Keywords

Comments

The initial seed + .5'i + .5'ii' + .5'ij' + .5'ik' can be seen as an element of the space Q X C_3 where Q are the quaternions.
Floretion Algebra Multiplication Program, FAMP Code: 2baseisumseq[ + .5'i + .5'ii' + .5'ij' + .5'ik']. SumType is set to: sum[Y[15]]

Links

Crossrefs

Cf. A108618, A110279, A110280, A110282, A110283.

A110280 A floretion-generated sequence calculated using the same rules given for A108618 with initial seed x = + .5'i + .5'ii' + .5'ij' + .5'ik'; version: "ibase".

Original entry on oeis.org

1, 1, 2, 1, 0, -2, -3, -3, -2, 4, 5, 11, 10, 7, 4, -6, -7, -13, -10, -3, -1, 12, 12, 17, 15, 8, 3, -7, -10, -14, -11, -4, 1, 13, 14, 20, 11, 11, -4, -11, -13, -24, -7, -11, 8, 16, 19, 29, 13, 14, -7, -13, -18, -26, -8, -9, 11, 22, 22, 35, 15, 15, -7, -20, -24, -35, -17, -13, 11, 26, 34, 43, 27, 19, -7, -24, -36, -43, -29, -17, 11
Offset: 0

Views

Author

Creighton Dement, Jul 18 2005

Keywords

Comments

The initial seed + .5'i + .5'ii' + .5'ij' + .5'ik' can be seen as an element of the space Q X C_3 where Q are the quaternions.
Floretion Algebra Multiplication Program, FAMP Code: 2ibasesumseq[ + .5'i + .5'ii' + .5'ij' + .5'ik']. SumType is set to: sum[Y[15]]

Crossrefs

Cf. A108618, A110279, A110281, A110282, A110283.

A110282 A floretion-generated sequence calculated using the same rules given for A108618 with initial seed x = + .5'i + .5'ii' + .5'ij' + .5'ik'; version: "ves".

Original entry on oeis.org

2, 0, -2, -5, -6, -5, -1, 3, 8, 15, 5, 1, -7, -16, -17, -20, -4, 2, 12, 22, 12, 17, 4, -6, -14, -24, -20, -16, -5, 2, 15, 25, 17, 15, 2, -7, -25, -19, -29, -21, 3, 1, 31, 21, 28, 23, -3, -8, -36, -28, -34, -18, 3, 5, 40, 28, 28, 23, -6, -6, -43, -38, -38, -29, 0, 8, 45, 44, 44, 31, 2, -14, -51, -54, -54, -37, -8, 16, 53, 60, 60, 39, 10
Offset: 0

Views

Author

Creighton Dement, Jul 18 2005

Keywords

Comments

The initial seed + .5'i + .5'ii' + .5'ij' + .5'ik' can be seen as an element of the space Q X C_3 where Q are the quaternions.
Floretion Algebra Multiplication Program, FAMP Code: 1vessumseq[ + .5'i + .5'ii' + .5'ij' + .5'ik']. SumType is set to: sum[Y[15]]

Crossrefs

Cf. A108618, A110279, A110280, A110281, A110283.

A272693 a(0)=0; thereafter, a(n) = (A108618(n-1)-3*A108619(n))/2.

Original entry on oeis.org

0, -1, -2, -5, -4, -3, -3, 0, 5, 2, -3, -6, -7, -5, 2, 9, 4, -5, -10, -9, -3, 6, 11, 5, -10, -21, -12, 5, 14, 9, -5, -19, -17, -4, 15, 16, 1, -15, -21, -12, 11, 20, 9, -11, -25, -17, 2, 21, 16, -5, -22, -21, -3, 18, 23, 5, -22, -33, -15, 18, 35, 17, -22, -45, -24, 17, 38, 21, -17, -43, -29, 8, 39
Offset: 0

Views

Author

N. J. A. Sloane, Jun 07 2016

Keywords

Links

Crossrefs

Cf. A108618, A108619.

Programs

  • Maple
    M:=1000;
a:=Array(0..M,0); # A108618 (with different offset)
b:=Array(0..M,0); # A108619 (with different offset)
c:=Array(0..M,0); # A272693
f:=n->sign(n)*(n mod 2);
a[0]:=0; b[0]:=0; c[0]:=0;
for n from 1 to M do
b[n]:=1+(a[n-1]+b[n-1])/2;
a[n]:=1+c[n-1]+f(c[n-1])+3*f(b[n]-1);
c[n]:=(a[n]-3*b[n])/2;
od:
[seq(a[n],n=0..M)];
[seq(b[n],n=0..M)];
[seq(c[n],n=0..M)];

A108620 2*a(n) = A108618(n) + 3*A108619(n).

Original entry on oeis.org

2, 4, 4, 2, 0, -3, -6, -4, 2, 6, 6, 2, -5, -10, -6, 4, 10, 8, 0, -9, -12, -4, 11, 20, 12, -6, -16, -10, 6, 19, 17, 1, -16, -18, -2, 16, 21, 9, -12, -22, -10, 12, 25, 17, -5, -22, -18, 4, 22, 20, 0, -21, -24, -4, 23, 32, 12, -21, -36, -16, 23, 44, 24, -18, -40, -22, 18, 43, 29, -11, -40, -30, 10, 40, 32, -6, -39, -35, 3, 40, 40, 2, -36
Offset: 0

Views

Author

Creighton Dement, Jun 22 2005

Keywords

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1vessum(*)seq[ + .5'i + .5'j + .5'k + .5e]

Links

Crossrefs

Cf. A108618, A108619.

Programs

  • Mathematica
    a[0] = b[0] = 1;
f[n_] := Sign[n]*Mod[n, 2];
a[n_] := a[n] = (1/2)*(a[n-1] - 3*b[n-1]) + 3*f[(1/2)*(a[n-1] + b[n-1])] + f[(1/2)*(a[n-1] - 3*b[n-1])] + 1;
b[n_] := b[n] = (1/2)*(a[n-1] + b[n-1]) + 1;
A108620 = Table[(a[n] + 3*b[n])/2, {n, 0, 100}] (* Jean-François Alcover, Feb 25 2015, after Benoit Jubin *)

A110283 A floretion-generated sequence calculated using the same rules given for A108618 with initial seed x = + .5'i + .5'ii' + .5'ij' + .5'ik'; version: "ibasei".

Original entry on oeis.org

1, 1, 0, -1, -2, -2, -1, 1, 2, 6, 5, 1, 0, -5, -6, -8, -5, 1, 2, 9, 7, 6, 6, -1, -3, -8, -9, -7, -4, 0, 3, 10, 9, 7, 4, 0, -7, -9, -8, -13, -1, 0, 7, 13, 8, 14, 3, -1, -9, -14, -11, -13, 0, 0, 10, 17, 9, 14, 2, -1, -9, -19, -13, -16, -4, 1, 11, 21, 17, 18, 6, -1, -13, -23, -21, -20, -8, 1, 15, 25, 25, 22, 10, -1, -17, -27, -29, -24, -12, 1, 19
Offset: 0

Views

Author

Creighton Dement, Jul 18 2005

Keywords

Comments

The initial seed + .5'i + .5'ii' + .5'ij' + .5'ik' can be seen as an element of the space Q X C_3 where Q are the quaternions.
Floretion Algebra Multiplication Program, FAMP Code: 2ibaseisumseq[ + .5'i + .5'ii' + .5'ij' + .5'ik']. SumType is set to: sum[Y[15]]

Crossrefs

Cf. A108618, A110279, A110280, A110281, A110282, A110284.

A108986 A floretion-generated sequence calculated using the rules given for A108618 with initial seed x = - .25'i + .25'j + .25'k - .25i' - .25j' - .25k' - .25'ii' + .25'jj' + .25'kk' - .25'ij' + .25'ik' - .25'ji' + .25'jk' + .25'ki' - .25'kj' + .25e; version: tes.

Original entry on oeis.org

1, -2, -9, -6, 1, 16, 12, -8, -18, -5, 22, 26, 15, -16, -20, -9, 40, 35, 12, -27, -21, 8, 49, 41, 11, -36, -21, 17, 72, 49, 10, -45, -18, 25, 88, 60, 4, -62, -23, 35, 107, 63, 3, -74, -19, 46, 127, 68, -2, -77, -21, 63, 137, 78, -14, -88, -22, 80, 151, 87, -26, -89, -23, 100, 162, 94, -29, -93, -21, 118, 169
Offset: 0

Views

Author

Creighton Dement, Jul 28 2005

Keywords

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4tessumseq[(- .5'i + .5'j + .5'k + .5e)*(- .5'ii' + .5'jj' + .5'kk' + .5e)], SumType is set to: sum[Y[15]] = sum[ * ]

Crossrefs

Cf. A108618.

A108930 A floretion-generated sequence calculated using the rules given for A108618 with initial seed x = + .25'i + .25'k + .25i' - .5j' + .75k' - .25'ij' - .25'ji' - .25'jk' + .25'kj' - .5e; version: basek.

Original entry on oeis.org

3, 0, 0, 2, 1, 0, 2, 1, 1, 2, 0, 1, 3, -1, 3, 0, 0, -1, 3, 3, -4, 5, 2, -6, 9, -1, -3, 5, 1, 0, 1, 1, 5, -3, -1, 8, -4, -2, 8, -2, -2, 6, -1, -2, 5, 0, -3, 5, 1, -2, 4, 2, -2, 0, 4, 1, -4, 6, 3, -8, 7, 4, -8, 5, 6, -7, 3, 7, -6, 3, 8, -8, 2, 8, -8, 4, 6, -5, 4, 4, -3, 3, 1, 0, 3, -2, 1, 3, -3, 2, 5, -6, 4, 6, -8, 5, 6, -10
Offset: 0

Views

Author

Creighton Dement, Jul 26 2005

Keywords

Comments

"Version: basek" in the name field is a reference to the floretion k'. It means that in order to calculate a(n), the rule given for A108618: "a(n) is given by twice the coefficient of e (the unit) in y from step 4 inside the n-th loop." should be replaced by "a(n) is given by 4 times the coefficient of k' in y from step 4 inside the n-th loop." This sequence appears to be unbounded. Moreover, (a(n)) produces a "spiral" when plotted against sequences from the same batch (i.e. against versions: tes, ves etc.). Ray-traced plots similar to the one given in the link can be formed using this sequence (for example). (a(n)) appears to become more "predictable" with increasing n. For n in the range from 987 to 1000 we have: a(987) = -59, a(988) = 112, a(989) = -52, a(990) = -55, a(991) = 108, a(992) = -51, a(993) = -53, a(994) = 109, a(995) = -55, a(996) = -51, a(997) = 107, a(998) = -54, a(999) = -50, a(1000) = 109
Floretion Algebra Multiplication Program, FAMP Code: 4baseksumseq[(+ .5'i - .25'j + .25'k + .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e)(+ .5'i + .5j' + .5'ij' + .5e)] Sumtype is set to: sum[Y[15]] = sum[ * ]

Links

Crossrefs

Cf. A108618.

A108619 A quaternion-generated sequence calculated using the rules given in the comment box with initial seed x = .5'i + .5'j + .5'k + .5e; version: "base".

Original entry on oeis.org

1, 2, 3, 2, 1, 0, -2, -3, 0, 3, 4, 3, 0, -4, -5, 0, 5, 6, 3, -2, -6, -5, 2, 10, 11, 2, -7, -8, -1, 8, 12, 6, -4, -11, -6, 5, 12, 10, 0, -11, -10, 1, 12, 14, 4, -8, -13, -4, 9, 14, 7, -6, -14, -9, 6, 18, 15, -2, -18, -17, 2, 22, 23, 2, -19, -20, -1, 20, 24, 6, -16, -23, -6, 17, 24, 9, -14, -24, -10, 14, 27, 14, -11, -24, -14, 10, 27, 18, -7
Offset: 0

Views

Author

Creighton Dement, Jun 22 2005

Keywords

Comments

Set y = x = .5'i + .5'j + .5'k + .5e Define a(0) = 1 (this is twice the coefficient of 'i in x), then "loop" steps 1-5 as described for A108618. a(n) is given by twice the coefficient of 'i (or 'j or 'k) in y from step 4 inside the n-th loop.

Links

Crossrefs

Cf. A108618, A108620, A272693.

Programs

  • Maple
    Floretion Algebra Multiplication Program, FAMP Code: 2ibasesum(*)seq[ + .5'i + .5'j + .5'k + .5e]
  • Mathematica
    a[0] = b[0] = 1;
f[n_] := Sign[n]*Mod[n, 2];
a[n_] := a[n] = (1/2)*(a[n-1] - 3*b[n-1]) + 3*f[(1/2)*(a[n-1] + b[n-1])] + f[(1/2)*(a[n-1] - 3*b[n-1])] + 1;
b[n_] := b[n] = (1/2)*(a[n-1] + b[n-1]) + 1;
A108619 = Table[b[n], {n, 0, 100}] (* Jean-François Alcover, Feb 25 2015, after Benoit Jubin *)
Showing 1-10 of 19 results. Next

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