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A357063
Lengths of the B blocks associated with A091787.
2
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
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
Sequence in context: A303863 A255836 A109454 * A307261 A287349 A000640
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