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 1-6 of 6 results.

A365367 Number of steps for iteration of map x -> (5/3)*round(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.

Original entry on oeis.org

3, 2, 1, 3, 15, 1, 2, 14, 1, 5, 2, 1, 13, 4, 1, 2, 4, 1, 5, 2, 1, 12, 3, 1, 2, 3, 1, 3, 2, 1, 3, 4, 1, 2, 4, 1, 11, 2, 1, 5, 6, 1, 2, 8, 1, 4, 2, 1, 4, 3, 1, 2, 3, 1, 3, 2, 1, 3, 5, 1, 2, 10, 1, 4, 2, 1, 4, 5, 1, 2, 6, 1, 7, 2, 1, 5, 3, 1, 2, 3, 1, 3, 2, 1, 3
Offset: 1

Views

Author

Chai Wah Wu, Sep 02 2023

Keywords

Comments

Conjecture: an integer will always be reached, i.e. a(n) > 0 for all n.

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365342, A365343.

Programs

  • Python
    from fractions import Fraction
def A365367(n):
    x, c = Fraction(n), 0
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x._round_(),3)
        c += 1
    return c

A365368 First integer > n reached under iteration of map x -> (5/3)*round(x) when started at n, or -1 if no such integer is ever reached.

Original entry on oeis.org

5, 5, 5, 20, 10245, 10, 20, 10245, 15, 130, 30, 20, 10245, 105, 25, 45, 130, 30, 245, 55, 35, 10245, 105, 40, 70, 120, 45, 130, 80, 50, 145, 245, 55, 95, 270, 60, 10245, 105, 65, 520, 870, 70, 120, 2605, 75, 355, 130, 80, 380, 230, 85, 145, 245, 90, 255, 155, 95
Offset: 1

Views

Author

Chai Wah Wu, Sep 02 2023

Keywords

Comments

Conjecture: an integer will always be reached, i.e. a(n) > 0 for all n.

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365341, A365342, A365367.

Programs

  • Python
    from fractions import Fraction
def A365368(n):
    x = Fraction(n)
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x._round_(),3)
    return int(x)

A365343 Record values of A087704.

Original entry on oeis.org

2, 4, 9, 10, 12, 17, 23, 29, 30, 32, 34, 38, 39, 40, 42, 43, 44, 47, 49, 52, 56, 57, 61, 62, 66, 71, 73, 75, 80
Offset: 1

Views

Author

Robert Israel, Sep 01 2023

Keywords

Comments

Numbers v = A087704(k) such that A087704(m) < v for 2 <= m < k.

Examples

			a(3) = 9 because A087704(10) = 9 and A087704(k) < 9 for 2 <= k < 10.

Crossrefs

Cf. A087704, A365342.

Programs

  • Maple
    g:= x -> 5/3 * floor(x):
h:= proc(n) local i,k;
  k:= g(n);
  for i from 1 while not (k::integer and k > n) do k:= g(k) od:
  i
end proc:
M:= 2: A:= 2: count:= 1:
for n from 3 while count < 17  do
  v:= h(n);
  if v > M then count:= count+1; A:= A,v; M:= v fi;
od:
A;

Formula

a(n) = A087704(A365342(n)).

Extensions

a(18)-a(21) from Chai Wah Wu, Sep 02 2023
a(22)-a(29) from Martin Ehrenstein, Sep 03 2023

A365369 A365368/5, except when A365368(n) = -1, then a(n) = -1.

Original entry on oeis.org

1, 1, 1, 4, 2049, 2, 4, 2049, 3, 26, 6, 4, 2049, 21, 5, 9, 26, 6, 49, 11, 7, 2049, 21, 8, 14, 24, 9, 26, 16, 10, 29, 49, 11, 19, 54, 12, 2049, 21, 13, 104, 174, 14, 24, 521, 15, 71, 26, 16, 76, 46, 17, 29, 49, 18, 51, 31, 19, 54, 151, 20, 34, 2049, 21, 99, 36
Offset: 1

Views

Author

Chai Wah Wu, Sep 02 2023

Keywords

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365341, A365342, A365367, A365368.

Programs

  • Python
    from fractions import Fraction
def A365369(n):
    x = Fraction(n)
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x._round_(),3)
    return int(x)//5

A365370 Positions of records in A365367.

Original entry on oeis.org

1, 5, 415, 635, 15935, 60971, 275039, 514661, 2857994, 14179544, 170794880, 2382918520
Offset: 1

Views

Author

Chai Wah Wu, Sep 02 2023

Keywords

Comments

Numbers k such that iteration of the map x -> (5/3)*round(x) starting at x = k takes more steps to reach an integer > k than it does for any number from 1 to k - 1.

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365341, A365342, A365367, A365368.

Formula

A365367(a(n)) = A365371(n).

A365371 Record values of A365367.

Original entry on oeis.org

3, 15, 17, 21, 24, 28, 32, 35, 37, 45, 50, 55
Offset: 1

Views

Author

Chai Wah Wu, Sep 02 2023

Keywords

Comments

Numbers v = A365367(k) such that A365367(m) < v for 1 <= m < k.

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365341, A365342, A365367, A365368, A365369, A365370.

Formula

a(n) = A365367(A365370(n)).
Showing 1-6 of 6 results.

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

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