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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A205840 [s(k)-s(j)]/2, where the pairs (k,j) are given by A205837 and A205838.

Original entry on oeis.org

1, 2, 1, 3, 6, 5, 4, 10, 9, 8, 4, 16, 13, 27, 26, 25, 21, 17, 44, 43, 42, 38, 34, 17, 71, 68, 55, 116, 115, 114, 110, 106, 89, 72, 188, 187, 186, 182, 178, 161, 144, 72, 304, 301, 288, 233, 493, 492, 491, 487, 483, 466, 449, 377, 305, 798, 797, 796, 792, 788
Offset: 1

Views

Author

Clark Kimberling, Feb 01 2012

Keywords

Comments

Let s(n)=F(n+1), where F=A000045 (Fibonacci numbers), so that s=(1,2,3,5,8,13,21,...). If c is a positive integer, there are infinitely many pairs (k,j) such that c divides s(k)-s(j). The set of differences s(k)-s(j) is ordered as a sequence at A204922. Guide to related sequences:
c....k..........j..........s(k)-s(j)....[s(k)-s(j)]/c
2....A205837....A205838....A205839......A205840
3....A205842....A205843....A205844......A205845
4....A205847....A205848....A205849......A205850
5....A205852....A205853....A205854......A205855
6....A205857....A205858....A205859......A205860
7....A205862....A205863....A205864......A205865
8....A205867....A205868....A205869......A205870
9....A205872....A205873....A205874......A205875
10...A205877....A205878....A205879......A205880

Examples

			The first six terms match these differences:
s(3)-s(1) = 3-1 = 2 = 2*1
s(4)-s(1) = 5-1 = 4 = 2*2
s(4)-s(3) = 5-3 = 2 = 2*1
s(5)-s(2) = 8-2 = 6 = 2*3
s(6)-s(1) = 13-1 = 12 = 2*6
s(6)-s(3) = 13-3 = 10 = 2*5

Crossrefs

Cf. A204890, A205587, A205839.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 2; t = d[c]    (* A205556 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]    (* A205837 *)
Table[j[n], {n, 1, z2}]    (* A205838 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205839 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205840 *)

A204924 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k)=A000045(k+1) (Fibonacci numbers).

Original entry on oeis.org

2, 3, 4, 4, 5, 5, 5, 6, 7, 6, 6, 6, 7, 9, 12, 7, 9, 7, 7, 7, 8, 10, 12, 12, 9, 8, 9, 10, 8, 17, 8, 8, 8, 9, 21, 12, 14, 10, 18, 17, 11, 9, 10, 10, 12, 12, 9, 12, 13, 9, 17, 9, 9, 9, 10, 17, 12, 12, 25, 22
Offset: 1

Views

Author

Clark Kimberling, Jan 21 2012

Keywords

Comments

See A204892 for a discussion and guide to related sequences.

Examples

			1 divides s(2)-s(1), so a(1)=2
2 divides s(3)-s(1), so a(2)=3
3 divides s(4)-s(2), so a(3)=4
9 divides s(7)-s(3), so a(9)=7

Links

Crossrefs

Cf. A000045, A204892.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 300; z2 = 60;
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
Table[d[n], {n, 1, z2}]   (* A204923 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
Table[k[n], {n, 1, z2}]       (* A204924 *)
Table[j[n], {n, 1, z2}]       (* A204925 *)
Table[s[k[n]], {n, 1, z2}]    (* A204926 *)
Table[s[j[n]], {n, 1, z2}]    (* A204927 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204928 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204929 *)

A205842 Numbers k for which 3 divides s(k)-s(j) for some j

Original entry on oeis.org

4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21
Offset: 1

Views

Author

Clark Kimberling, Feb 01 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(4)-s(2) = 5-2 = 3
s(5)-s(2) = 8-2 = 6
s(5)-s(4) = 8-5 = 3
s(6)-s(1) = 13-1 = 12
s(7)-s(3) = 21-3 = 18
s(8)-s(1) = 34-1 = 33

Crossrefs

Cf. A204892, A205845.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 3; t = d[c]       (* A205841 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]      (* A205842 *)
Table[j[n], {n, 1, z2}]      (* A205843 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205844 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205845 *)

A205845 [s(k)-s(j)]/3, where the pairs (k,j) are given by A205842 and A205843, and s(k) denotes the (k+1)-st Fibonacci number.

Original entry on oeis.org

1, 2, 1, 4, 6, 11, 7, 18, 14, 7, 29, 28, 27, 47, 41, 77, 76, 75, 48, 125, 124, 123, 96, 48, 203, 199, 192, 185, 328, 322, 281, 532, 528, 521, 514, 329, 861, 857, 850, 843, 658, 329, 1393, 1392, 1391, 1364, 1316, 1268, 2254, 2248, 2207, 1926, 3648
Offset: 1

Views

Author

Clark Kimberling, Feb 01 2012

Keywords

Comments

For a guide to related sequences, see A205840.
The first six terms match these differences:
s(4)-s(2) = 5-2 = 3 = 3*1
s(5)-s(2) = 8-2 = 6 = 3*2
s(5)-s(4) = 8-5 = 3 = 3*1
s(6)-s(1) = 13-1 = 12 = 3*4
s(7)-s(3) = 21-3 = 18 = 3*6
s(8)-s(1) = 34-1 = 33 + 3*11
(See the program at A205842.)

Examples

			The first six terms match these differences:
s(4)-s(2) = 5-2 = 3 = 3*1
s(5)-s(2) = 8-2 = 6 = 3*2
s(5)-s(4) = 8-5 = 3 = 3*1
s(6)-s(1) = 13-1 = 12 = 3*4
s(7)-s(3) = 21-3 = 18 = 3*6
s(8)-s(1) = 34-1 = 33 + 3*11

Crossrefs

Cf. A204890, A205842, A205845.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 3; t = d[c]       (* A205841 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]      (* A205842 *)
Table[j[n], {n, 1, z2}]      (* A205843 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205844 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205845 *)

A205847 Numbers k for which 4 divides s(k)-s(j) for some j

Original entry on oeis.org

4, 6, 6, 7, 7, 7, 8, 9, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(4)-s(1) = 5-1 = 4
s(6)-s(1) = 13-1 = 12
s(6)-s(4) = 13-5 = 8
s(7)-s(1) = 21-1 = 20
s(7)-s(4) = 21-5 = 16
s(7)-s(6) = 21-13 = 8

Crossrefs

Cf. A204892, A205850.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]     (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 4; t = d[c]    (* A205846 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]    (* A205847 *)
Table[j[n], {n, 1, z2}]    (* A205848 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205849 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205850 *)

A205852 Numbers k for which 5 divides s(k)-s(j) for some j

Original entry on oeis.org

5, 6, 6, 7, 9, 10, 11, 11, 12, 12, 12, 13, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(5)-s(3) = 8-3 = 5
s(6)-s(3) = 13-3 = 10
s(6)-s(5) = 13-8 = 5
s(7)-s(1) = 21-1 = 20
s(9)-s(4) = 55-5 = 50
s(10)-s(8) = 89-34 = 55

Crossrefs

Cf. A204892, A205855.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]    (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 5; t = d[c]    (* A205851 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}] (* A205852 *)
Table[j[n], {n, 1, z2}] (* A205853 *)
Table[s[k[n]]-s[j[n]], {n, 1, z2}](* A205854 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205855 *)

A205857 Numbers k for which 6 divides s(k)-s(j) for some j

Original entry on oeis.org

5, 6, 7, 9, 9, 10, 12, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(5)-s(2) = 8-2 = 6 = 6*1
s(6)-s(1) = 13-1 = 12 = 6*2
s(7)-s(3) = 21-3 = 18 = 6*3
s(9)-s(1) = 55-1 = 54 = 6*9
s(9)-s(6) = 55-13 = 42 = 6*7
s(10)-s(4) = 89-5 = 84 =6*14

Crossrefs

Cf. A204892, A205857, A205860.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 6; t = d[c]    (* A205856 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]     (* A205857 *)
Table[j[n], {n, 1, z2}]     (* A205858 *)
Table[s[k[n]]-s[j[n]], {n, 1, z2}]    (* A205859 *)
Table[(s[k[n]]-s[j[n]])/c, {n,1,z2}]  (* A205860 *)

A205862 Numbers k for which 7 divides s(k)-s(j) for some j

Original entry on oeis.org

5, 8, 9, 9, 10, 12, 13, 13, 13, 14, 14, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 19, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 27, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(5)-s(1) = 8-1 = 7 = 7*1
s(8)-s(6) = 34-13 = 21 = 7*3
s(9)-s(6) = 55-13 = 42 = 7*6
s(9)-s(8) = 55-34 = 21 = 7*3
s(10)-s(4) = 89-5 = 84 = 7*12
s(13)-s(6) = 377-13 = 364 =7*52

Crossrefs

Cf. A204892, A205863, A205865.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]    (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 7; t = d[c]   (* A205861 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]    (* A205862 *)
Table[j[n], {n, 1, z2}]    (* A205863 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205864 *)
Table[(s[k[n]]-s[j[n]])/c, {n,1,z2}] (* A205865 *)

A205867 Numbers k for which 8 divides s(k)-s(j) for some j

Original entry on oeis.org

6, 7, 7, 8, 10, 11, 12, 12, 13, 13, 13, 14, 14, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(6)-s(4) = 13-5 = 8 = 8*1
s(7)-s(4) = 21-5 = 16 = 8*2
s(7)-s(6) = 21-13 = 8 = 8*1
s(8)-s(2) = 34-2 = 32 = 8*4
s(10)-s(1) = 89-1 = 88 = 8*11
s(11)-s(5) = 144-8 = 136 =8*17

Crossrefs

Cf. A204892, A205868, A205870.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 8; t = d[c]    (* A205866 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]      (* A205867 *)
Table[j[n], {n, 1, z2}]        (* A205868 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205869 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205870 *)

A205872 Numbers k for which 9 divides s(k)-s(j) for some j

Original entry on oeis.org

7, 9, 10, 12, 12, 13, 13, 13, 14, 16, 17, 17, 18, 19, 20, 21, 21, 21, 21, 22, 22, 22, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 29, 29, 29, 30, 30, 31, 31, 31, 32, 32
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(7)-s(3) = 21-3 = 18 = 9*2
s(9)-s(1) = 55-1 = 54 = 9*6
s(10)-s(5) = 89-8 = 81 = 9*9
s(12)-s(5) = 233-8 = 225 = 9*25
s(12)-s(10) = 233-89 = 144 = 9*16
s(13)-s(5) = 377-8 = 369 =9*41

Crossrefs

Cf. A204892, A205873, A205875.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 9; t = d[c]     (* A205871 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]       (* A205872 *)
Table[j[n], {n, 1, z2}]         (* A205873 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]   (* A205874 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205875 *)
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