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.

A218828 Reluctant sequence of reverse reluctant sequence A004736.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 3, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 3, 2, 1, 4, 1, 2, 1, 3, 2, 1, 4, 3, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2
Offset: 1

Views

Author

Boris Putievskiy, Dec 15 2012

Keywords

Comments

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A.
Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.
Sequence A004736 is the reverse reluctant sequence of sequence 1,2,3,... (A000027).

Examples

			The start of the sequence as triangle array T(n,k) is:
  1;
  1,2;
  1,2,1;
  1,2,1,3;
  1,2,1,3,2;
  1,2,1,3,2,1;
  ...

Links

Crossrefs

Cf. A004736, A002260, A220280.

Programs

  • Python
    t=int((math.sqrt(8*n-7) - 1)/ 2)
n1=n-t*(t+1)/2
t1=int((math.sqrt(8*n1-7) - 1)/ 2)
m=(t1*t1+3*t1+4)/2-n1

Formula

T(n,k) = A004736(k) for every n.
As a linear array, the sequence is a(n) = (t1^2+3*t1+4)/2-n1, where n1=n-t(t+1)/2, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2].

A220464 Reverse reluctant sequence of reluctant sequence A002260.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 3, 2, 1, 2, 1, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 4, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 5, 4, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 1, 5, 4, 3
Offset: 1

Views

Author

Boris Putievskiy, Dec 15 2012

Keywords

Comments

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A.
Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.
Sequence A002260 is the reluctant sequence of sequence 1,2,3,... (A000027).

Examples

			The start of the sequence as triangle array T(n,k) is:
  1;
  1,1;
  2,1,1;
  1,2,1,1;
  2,1,2,1,1;
  3,2,1,2,1,1;
  ...

Links

Crossrefs

Cf. A002260, A004736, A220280.

Programs

  • Python
    t=int((math.sqrt(8*n-7) - 1)/ 2)
n1=(t*t+3*t+4)/2-n
t1=int((math.sqrt(8*n1-7) - 1)/ 2)
m=n1-t1*(t1+1)/2

Formula

T(n,k) = A002260(n-k+1).
As a linear array, the sequence is a(n) = n1-t1*(t1+1)/2, where n1=(t*t+3*t+4)/2-n, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2].

A220465 Reverse reluctant sequence of reverse reluctant sequence A004736.

Original entry on oeis.org

1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 4, 1, 2, 3, 1, 2, 1, 3, 4, 1, 2, 3, 1, 2, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 6, 1, 2, 3
Offset: 1

Views

Author

Boris Putievskiy, Dec 15 2012

Keywords

Comments

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A.
Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.
Sequence A004736 is the reverse reluctant sequence of sequence 1,2,3,... (A000027).

Examples

			The start of the sequence as triangle array T(n,k) is:
  1;
  2,1;
  1,2,1;
  3,1,2,1;
  2,3,1,2,1;
  1,2,3,1,2,1;
  ...

Links

Crossrefs

Cf. A000027, A004736, A002260, A220280.

Programs

  • Python
    t=int((math.sqrt(8*n-7) - 1)/ 2)
n1=(t*t+3*t+4)/2-n
t1=int((math.sqrt(8*n1-7) - 1)/ 2)
m=(t1*t1+3*t1+4)/2-n1

Formula

T(n,k) = A004736(n-k+1).
As a linear array, the sequence is a(n) = (t1*t1+3*t1+4)/2-n1, where n1=(t*t+3*t+4)/2-n, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2].
Showing 1-3 of 3 results.

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