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 1-5 of 5 results.

A110766 Fractalization of Pi.

Original entry on oeis.org

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

Views

Author

Alexandre Wajnberg, Sep 15 2005

Keywords

Comments

Self-descriptive sequence: even terms are the sequence itself, odd terms are the digits of the decimal expansion of Pi.

Links

Crossrefs

Cf. A000796 (Pi), A003602.
Cf. A110779 (of e), A110812 (of sqrt 2), A382130 (of phi).

Programs

  • Haskell
    import Data.List (transpose)
a110766 n = a110766_list !! (n-1)
a110766_list = concat $ transpose [a000796_list, a110766_list]
-- Reinhard Zumkeller, Aug 29 2014

Formula

a(2n) = a(n); a(2n-1) = digits of Pi.

Extensions

a(85) corrected and formula fixed by Reinhard Zumkeller, Aug 29 2014

A110779 Fractalization of e.

Original entry on oeis.org

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

Views

Author

Alexandre Wajnberg, Sep 15 2005

Keywords

Comments

Self-descriptive sequence: even terms are the sequence itself, odd terms are the digits of the decimal expansion of e.

Links

Crossrefs

Cf. A001113, A003602.
Cf. A110766 (of Pi), A110812 (of sqrt 2), A382130 (of phi).

Formula

a(2n) = a(n); a(2n+1) = digits of e.

A110812 Fractalization of sqrt 2.

Original entry on oeis.org

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

Views

Author

Alexandre Wajnberg, Sep 15 2005

Keywords

Comments

Self-descriptive sequence: even terms are the sequence itself, odd terms are the digits of the decimal expansion of sqrt 2.

Links

Crossrefs

Cf. A002193 (sqrt 2), A003602.
Cf. A110766 (of Pi), A110779 (of e), A382130 (of phi).

Formula

a(2n)=a(n); a(2n+1)=digits of sqrt 2.

A382128 Fractalization of the Recamán sequence.

Original entry on oeis.org

0, 0, 1, 0, 3, 1, 6, 0, 2, 3, 7, 1, 13, 6, 20, 0, 12, 2, 21, 3, 11, 7, 22, 1, 10, 13, 23, 6, 9, 20, 24, 0, 8, 12, 25, 2, 43, 21, 62, 3, 42, 11, 63, 7, 41, 22, 18, 1, 42, 10, 17, 13, 43, 23, 16, 6, 44, 9, 15, 20, 45, 24, 14, 0, 46, 8, 79, 12, 113, 25, 78, 2, 114, 43, 77, 21, 39, 62, 78
Offset: 1

Views

Author

David Cleaver, Mar 16 2025

Keywords

Comments

Self-descriptive sequence: even indexed terms are the sequence itself, odd indexed terms are the Recamán sequence.
This is an r1k1 fractal sequence, where r1k1 means: remove 1 term, keep 1 term, repeat. The Removed terms are the sequence that has been fractalized, and the Kept terms are the original fractal sequence.
This fractal sequence is not a Kimberling fractal sequence because if you delete the first occurrence of each term, the remaining sequence is not the same as the original. This sequence fails to be a Kimberling fractal due to having consecutive terms that both appeared earlier in the sequence, starting with the 1 and 42 at index 48 and 49, respectively.

Links

Crossrefs

Cf. A005132, A003602, A110766, A110779, A110812, A382129, A382130.

Formula

a(2n) = a(n); a(2n-1) = A005132(n), n >= 1.
a(n) = A005132(A003602(n)).

A382129 Fractalization of the prime numbers.

Original entry on oeis.org

2, 2, 3, 2, 5, 3, 7, 2, 11, 5, 13, 3, 17, 7, 19, 2, 23, 11, 29, 5, 31, 13, 37, 3, 41, 17, 43, 7, 47, 19, 53, 2, 59, 23, 61, 11, 67, 29, 71, 5, 73, 31, 79, 13, 83, 37, 89, 3, 97, 41, 101, 17, 103, 43, 107, 7, 109, 47, 113, 19, 127, 53, 131, 2, 137, 59, 139, 23, 149, 61, 151, 11, 157
Offset: 1

Views

Author

David Cleaver, Mar 16 2025

Keywords

Comments

Self-descriptive sequence: even indexed terms are the sequence itself, odd indexed terms are the prime numbers.
This is an r1k1 fractal sequence, where r1k1 means: remove 1 term, keep 1 term, repeat. The Removed terms are the sequence that has been fractalized, and the Kept terms are the original fractal sequence.
This fractal sequence is also a Kimberling fractal sequence because if you delete the first occurrence of each term, the remaining sequence is the same as the original.

Links

Crossrefs

Cf. A000040, A003602, A110766, A110779, A110812, A382128, A382130.

Programs

  • Mathematica
    a[n_] := Prime[(n/2^IntegerExponent[n, 2] + 1)/2]; Array[a, 100] (* Amiram Eldar, Mar 21 2025 *)

Formula

a(2n) = a(n); a(2n-1) = A000040(n), n >= 1.
a(n) = A000040(A003602(n)).
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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