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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A359737 Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = A296239(a(n)) has the same sequence of digits, where A296239 gives the distance from the nearest Fibonacci number, cf. A000045.

Original entry on oeis.org

0, 12, 10, 4, 1, 17, 6, 7, 41, 27, 48, 25, 9, 11, 62, 30, 42, 15, 26, 43, 14, 20, 28, 19, 16, 2, 38, 23, 22, 29, 32, 40, 51, 18, 33, 59, 36, 3, 53, 47, 35, 46, 54, 49, 57, 24, 63, 87, 31, 91, 111, 64, 37, 113, 5, 39, 56, 88, 81, 52, 58, 50, 80, 86, 61, 92, 60, 141, 85, 82, 147
Offset: 0

Views

Author

M. F. Hasler and Eric Angelini, Jan 12 2023

Keywords

Comments

In the definition, "has the same sequence of digits" means that the concatenation of the terms yields the same string of digits, for the sequence a(.) and the sequence d(.).
Conjectured to be a permutation of the nonnegative integers. The inverse permutation would start (0, 4, 25, 37, 3, 54, 6, 7, 104, 12, 2, 13, 1, 106, 20, ...).

Examples

			Below, row "F" lists the closest Fibonacci number to a(n) and row "d" the absolute difference |a(n) - F|. We have the same sequence of digits in rows a (this sequence) and d:
  n :  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14 ...
  a :  0  12  10   4   1  17   6   7  41  27  48  25   9  11  62 ...
  F :  0  13   8   3   1  13   5   8  34  21  55  21   8  13  55 ...
  d :  0   1   2   1   0   4   1   1   7   6   7   4   1   2   7 ...

Links

  • Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023.
  • Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023. [Cached copy]

Crossrefs

Cf. A296239 (distance from the nearest Fibonacci number), A000045 (the Fibonacci numbers).
Cf. A359734, A359736 (similar for primes and squares).

Programs

  • PARI
    spine(fibonacci, 200) \\ \\ See A359734 for spine()

A309416 a(n) = Sum_{k > 0} d^k(n), where d^k corresponds to the k-th iterate of A296239.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 3, 5, 3, 2, 1, 0, 1, 2, 3, 5, 5, 7, 7, 5, 5, 3, 2, 1, 0, 1, 2, 3, 5, 5, 7, 8, 8, 10, 12, 12, 10, 8, 8, 7, 5, 5, 3, 2, 1, 0, 1, 2, 3, 5, 5, 7, 8, 8, 10, 12, 13, 13, 13, 15, 17, 19, 22, 19, 17, 15, 13, 13, 13, 12
Offset: 0

Views

Author

Rémy Sigrist, Jul 30 2019

Keywords

Comments

Iterating A296239 from any nonnegative number always leads to the fixed point 0, hence the series in the name has only finitely many nonzero terms and is well defined.

Examples

			For n = 1024:
- A296239(1024) = 37,
- A296239(37) = 3,
- A296239(3) = 0,
- hence a(1024) = 37 + 3 = 40.

Links

Crossrefs

Cf. A000045, A296239.

Programs

  • PARI
    A296239(n) = for (i=1, oo, if (n<=fibonacci(i), return (min(n-fibonacci(i-1), fibonacci(i)-n))))
a(n) = my (v=0); while (n=A296239(n), v+=n); return (v)

Formula

a(n) = 0 iff n is a Fibonacci number.

A301297 Distance from n to nearest Catalan number.

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33
Offset: 1

Views

Author

N. J. A. Sloane, Mar 24 2018

Keywords

Crossrefs

Cf. A000108, A053188, A080732, A296239.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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