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 11-20 of 25 results. Next

A111614 First upper diagonal of array in A109626.

Original entry on oeis.org

1, 1, 1, 3, 1, 6, 1, 7, 1, 3, 1, 6, 1, 3, 12, 3, 1, 6, 1, 11, 18, 3, 1, 24, 1, 3, 1, 8, 1, 21, 1, 11, 20, 20, 23, 16, 1, 22, 34, 21, 1, 14, 1, 22, 24, 26, 1, 2, 1, 43, 6, 26, 1, 33, 17, 46, 43, 32, 1, 25, 1, 34, 47, 35, 63, 25, 1, 8, 49, 31, 1, 48, 1, 40, 32, 73, 21, 58, 1, 80, 28, 44, 1, 29
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Jul 30 2005

Keywords

Comments

a(1) = a(2) = 1 and a(p^e) = 1 for odd primes p and noncomposite exponents e.
a(81) = 28 and not 1 because 9^2 = 81.

Crossrefs

Cf. A109626.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[ g[n, n + 1], {n, 84}]

A111624 Second lower diagonal of A109626.

Original entry on oeis.org

1, 4, 5, 2, 7, 8, 3, 10, 11, 8, 13, 14, 5, 16, 17, 12, 19, 20, 14, 22, 23, 24, 25, 26, 9, 28, 29, 10, 31, 32, 33, 34, 35, 24, 37, 38, 26, 40, 41, 14, 43, 44, 15, 46, 47, 16, 49, 50, 51, 52, 53, 36, 55, 56, 38, 58, 59, 60, 61, 62, 63, 64, 65, 22, 67, 68, 46, 70, 71, 72, 73, 74, 75
Offset: 3

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

Keywords

Crossrefs

Cf. A109626.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[ g[n, n - 2], {n, 3, 75}]

A111626 T(2n, n)/n of A109626.

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 02 2005

Keywords

Comments

A sequence of just 1's and 2's.

Crossrefs

Cf. A109626.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[ g[2n, n]/n, {n, 80}]

A111628 T(2n, 2n-1)/n of A109626.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 02 2005

Keywords

Comments

A sequence of just 1's and 2's.

Crossrefs

Cf. A109626.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[ g[2n, 2n - 1]/n, {n, 72}]

A111629 a(n) = A109626(3n, n)/n.

Original entry on oeis.org

1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 2, 3, 3, 1, 3, 3, 3, 3, 3, 2, 3, 3, 1, 3, 3, 2, 3, 3, 2, 3, 3, 1, 3
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 02 2005

Keywords

Comments

A sequence of just 1's, 2's and 3's.

Crossrefs

Cf. A109626.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[ g[3n, n]/n, {n, 53}]

A111630 T(3n, 3n-2)/n of A109626.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 2, 3, 1, 1, 3, 2, 2, 1, 1, 1, 3, 2, 2, 3, 3, 1, 2, 3, 3, 2, 1, 3, 3, 1, 2, 1, 2, 2, 3, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 02 2005

Keywords

Comments

A sequence of just 1's, 2's and 3's.

Crossrefs

Cf. A109626.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[ g[3n, 3n - 2]/n, {n, 48}]

A111612 Twelfth column of A109626.

Original entry on oeis.org

1, 1, 1, 3, 5, 6, 7, 4, 6, 5, 11, 6, 13, 14, 5, 12, 17, 18, 19, 5, 21, 22, 23, 8, 25, 13, 9, 28, 29, 10, 31, 8, 33, 17, 35, 21, 37, 38, 26, 20, 41, 21, 43, 22, 45, 46, 47, 44, 49, 25, 34, 13, 53, 9, 55, 56, 19, 29, 59, 20, 61, 62, 42, 16, 65, 22, 67, 51, 23, 70, 71, 72, 73, 37, 75, 38
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

Keywords

Crossrefs

Cf. A109626.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[g[n, 12 + 1], {n, 76}]

A111625 n divided by the second lower diagonal of A109626 & 3/2 -> 2.

Original entry on oeis.org

3, 1, 1, 3, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Robert G. Wilson v, Aug 03 2005

Keywords

Comments

A sequence of just 1's, 2's and 3's.
a/A111624(n)=1 if n == 0,2 (Mod 3).
a(3n-2): 3,3,3,2,3,2,2,1,3,3,1,2,2,3,3,3,1,2,2,1,1,3,2,1,1,2,3,1,1,3,2,3,2,2,1,2,3,2,2,2,3,3,3,3,2,1,1,3

Crossrefs

Cf. A111624.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[ a[j], {j, 0, 144}]]; g[n_, m_] := f[n][[m]];Table[ Ceiling[ n/g[n, n - 2]], {n, 3, 108}]

A111603 Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the antidiagonal read from upper right to lower left.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 4, 1, 1, 2, 1, 2, 5, 1, 1, 2, 3, 4, 5, 6, 1, 1, 1, 3, 3, 5, 3, 7, 1, 1, 2, 3, 4, 5, 2, 7, 8, 1, 1, 2, 3, 4, 1, 3, 7, 4, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 3, 1, 5, 6, 7, 2, 3, 5, 11, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 1, 1, 3, 4, 5, 3, 1, 4, 9, 10
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

Keywords

Examples

			Table begins
k= 0 1 2 3 4 5 6 7 8 9 10 11 12 13
n\
1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2| 1 2 1 2 2 2 1 2 2 2 1 2 1 2
3| 1 3 3 1 3 3 3 3 3 3 3 3 1 3
4| 1 4 2 4 3 4 4 4 1 4 4 4 3 4
5| 1 5 5 5 5 1 5 5 5 5 4 5 5 5
6| 1 6 3 2 3 6 6 6 3 4 6 6 6 6
7| 1 7 7 7 7 7 7 1 7 7 7 7 7 7
8| 1 8 4 8 2 8 4 8 7 8 8 8 4 8
9| 1 9 9 3 9 9 3 9 9 1 9 9 6 9
10| 1 10 5 10 10 2 5 10 10 10 3 10 5 10
11| 1 11 11 11 11 11 11 11 11 11 11 1 11 11
12| 1 12 6 4 9 12 4 12 12 8 6 12 6 12
13| 1 13 13 13 13 13 13 13 13 13 13 13 13 1
14| 1 14 7 14 7 14 14 2 7 14 14 14 14 14
15| 1 15 15 5 15 3 10 15 15 10 15 15 5 15
16| 1 16 8 16 4 16 8 16 10 16 8 16 12 16

Crossrefs

Cf. A111613, A083952, A083953, A083954, A083945, A083946, A083947, A083948, A083949, A083950, A084066, A084067.
Cf. A109626, A111604.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[ a[j], {j, 0, 32}]]; g[n_, m_] := f[n][[m]]; Flatten[ Table[ f[i, n - i], {n, 15}, {i, n - 1, 1, -1}]]

A111604 Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the antidiagonal read zig-zag.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 4, 3, 2, 1, 1, 2, 1, 2, 5, 1, 1, 6, 5, 4, 3, 2, 1, 1, 1, 3, 3, 5, 3, 7, 1, 1, 8, 7, 2, 5, 4, 3, 2, 1, 1, 2, 3, 4, 1, 3, 7, 4, 9, 1, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 3, 1, 5, 6, 7, 2, 3, 5, 11, 1, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 3, 4, 5, 3, 1, 4, 9, 10, 11
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

Keywords

Comments

T(n,n)=T(n,n+2)=A111627.

Examples

			Table begins
\k...0...1....2....3....4....5....6....7....8....9...10...11...12...13
n\
1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2| 1 2 1 2 2 2 1 2 2 2 1 2 1 2
3| 1 3 3 1 3 3 3 3 3 3 3 3 1 3
4| 1 4 2 4 3 4 4 4 1 4 4 4 3 4
5| 1 5 5 5 5 1 5 5 5 5 4 5 5 5
6| 1 6 3 2 3 6 6 6 3 4 6 6 6 6
7| 1 7 7 7 7 7 7 1 7 7 7 7 7 7
8| 1 8 4 8 2 8 4 8 7 8 8 8 4 8
9| 1 9 9 3 9 9 3 9 9 1 9 9 6 9
10| 1 10 5 10 10 2 5 10 10 10 3 10 5 10
11| 1 11 11 11 11 11 11 11 11 11 11 1 11 11
12| 1 12 6 4 9 12 4 12 12 8 6 12 6 12
13| 1 13 13 13 13 13 13 13 13 13 13 13 13 1
14| 1 14 7 14 7 14 14 2 7 14 14 14 14 14
15| 1 15 15 5 15 3 10 15 15 10 15 15 5 15
16| 1 16 8 16 4 16 8 16 10 16 8 16 12 16

Crossrefs

Cf. A111613, A083952, A083953, A083954, A083945, A083946, A083947, A083948, A083949, A083950, A084066, A084067.
Cf. A109626, A111603.

Programs

  • Mathematica
    f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 32}]]; g[n_, m_] := f[n][[m]];
Previous Showing 11-20 of 25 results. Next

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