A357063 Lengths of the B blocks associated with A091787.

1, 4, 13, 42, 127, 382, 1149, 3448, 10345, 31044, 93133, 279400, 838203, 2514610, 7543831, 22631496, 67894489, 203683468, 611050413, 1833151240, 5499453721, 16498361166, 49495083499, 148485250498, 445455751497, 1336367254492, 4009101763477, 12027305290463, 36081915871390, 108245747614173, 324737242842520, 974211728527561, 2922635185582686, 8767905556748059, 26303716670244178, 78911150010732543, 236733450032197630, 710200350096592891

Offset

1,2

Comments

The B blocks are explained in the article "A slow-growing sequence defined by an unusual occurrence". They have superscript (2).

Links

Table of n, a(n) for n=1..38.

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), Article 07.1.2.

Example

The third B-block of order 2 is B_3^{(2)}=2223222322233. Therefore, a(3)=13.

Prog

(Python)
number_of_terms=38
def Cn(X):
    l=len(X)
    cn=1
    for i in range(1, int(l/2)+1):
        j=i
        while(X[l-j-1]==X[l-j-1+i]):
            j=j+1
            if j>=l:
                break
        candidate=int(j/i)
        if candidate>cn:
            cn=candidate
    return cn
# This algorithm generates a prefix of the level-3 Gijswijt sequence
def Generate_A3(number):
  glue_lengths=[]
  A3=[3]
  S=[3]
  i=0
  while(True):
      c=Cn(A3)
      if c<3:
        glue_lengths.append(len(S))
        i=i+1
        if i==number:
            break
        S=[]
      A3.append(max(c, 3))
      S.append(max(c, 3))
  return glue_lengths
glue_lengths=Generate_A3(number_of_terms-1)
beta_lengths=[1]
beta_length=1
for l in glue_lengths:
    beta_length=3*beta_length+l
    beta_lengths.append(beta_length)
print(beta_lengths)

Crossrefs

Cf. A091787, A357068.

Sequence in context: A303863 A255836 A109454 * A307261 A287349 A000640

Adjacent sequences: A357060 A357061 A357062 * A357064 A357065 A357066

Keyword

nonn

Author

Levi van de Pol, Sep 10 2022

Extensions

By special permission, more than the usual number of terms are shown. - N. J. A. Sloane, Oct 23 2022

Status

approved