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.

A091588 A smoothed version of A091587.

Original entry on oeis.org

1, 3, 8, 24, 67, 195, 580, 1730, 5179, 15533, 46578, 139712, 419115, 1257319, 3771930, 11315764, 33947261, 101841751, 305525228, 916575642, 2749726883
Offset: 0

Views

Author

N. J. A. Sloane, Mar 05 2004

Keywords

Comments

Each term is roughly 3 times the previous term.

Crossrefs

Records in A091839. Cf. A090822, A091587, A091587, A217590.

Formula

a(n+1) = a(n) + A357063(n+1) + A091840(n+1). See Conjecture 4.2 of F. J. van de Bult et al., proved p. 54 of Levi van de Pol. - Levi van de Pol, Nov 04 2022

Extensions

a(10)-a(13) from Allan Wilks, Mar 10 2004
a(14)-a(20) from Alexander Staunton, Apr 09 2022
Removed an incorrect program. - N. J. A. Sloane, Aug 20 2022

A091579 Lengths of suffix blocks associated with A090822.

Original entry on oeis.org

1, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 67, 1, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 196, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 68, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 581, 3, 1, 9, 4, 25, 3, 1, 9, 4, 67, 1, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 196, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 68, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 1731, 3, 1, 9, 4, 24
Offset: 1

Views

Author

N. J. A. Sloane, Mar 05 2004

Keywords

Comments

The suffix blocks are what is called "glue string" in the paper by Gijswijt et al (2007). Roughly speaking, these are the terms >= 2 appended before the sequence (A090822) goes on with a(n+1) = 1 followed by all other initial terms a(2..n), cf. Example. The concatenation of these glue strings yields A091787. - M. F. Hasler, Aug 08 2018

Examples

			From _M. F. Hasler_, Aug 09 2018: (Start)
In sequence A090822, after the initial (1, 1) follows the first suffix block or glue string (2) of length a(1) = 1. This is followed by A090822(4) = 1 which indicates that the suffix block has ended, and the whole sequence A090822(1..3) up to and including this suffix block is repeated: A090822(4..6) = A090822(1..3).
Then A090822 goes on with (2, 2, 3, 1, ...), which tells that the second suffix block is A090822(7..9) = (2, 2, 3) of length a(2) = 3, whereafter the sequence starts over again: A090822(10..18) = A090822(1..9). (End)
		

Crossrefs

Cf. A090822, A091587 (records). For a smoothed version see A091839.
Cf. A091787 for the concatenation of the glue strings.

Programs

  • Python
    # compute curling number of L
    def curl(L):
        n = len(L)
        m = 1 #max nr. of repetitions at the end
        k = 1 #length of repeating block
        while(k*(m+1) <= n):
            good = True
            i = 1
            while(i <= k and good):
                for t in range(1, m+1):
                    if L[-i-t*k] != L[-i]:
                        good = False
                i = i+1
            if good:
                m = m+1
            else:
                k = k+1
        return m
    # compute lengths of first n glue strings
    def A091579_list(n):
        Promote = [1] #Keep track of promoted elements
        L = [2]
        while len(Promote) <= n:
            c = curl(L)
            if c < 2:
                Promote = Promote+[len(L)+1]
                c = 2
            L = L+[c]
        return [Promote[i+1]-Promote[i] for i in range(n)]
    # Dion Gijswijt, Oct 08 2015

A217590 Values in A091579 that need to be smoothed in order to produce A091588.

Original entry on oeis.org

4, 9, 25, 68, 196, 581, 1731, 5180, 15534, 46579, 139713, 419116, 1257320
Offset: 1

Views

Author

N. J. A. Sloane, Mar 18 2013

Keywords

Comments

a(n) = A091588(n) + 1 for n >= 1.
Each term is roughly 3 times the previous term.

Crossrefs

Formula

I would very much like a formula for this sequence!
Showing 1-3 of 3 results.