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A091842
Lengths of suffix blocks associated with A091799.
2
1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 10, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 10, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 10, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 42, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 10, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 10
OFFSET
1,4
COMMENTS
The suffix blocks are what is called "glue string" in the paper by Gijswijt et al. (2007). Roughly speaking, these are the terms appended before the sequence goes on with a copy of all its initial terms up to the current position. (In the present sequence, when this happens, then this initial segment will actually be repeated for a total of 4 copies. Therefore each suffix block will start with a "4".) - M. F. Hasler, Aug 08 2018
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), #07.1.2.
FORMULA
a(n) = A091843(valuation(n-1,4)) for n < 259. For larger n, the index n must be increased by the number of terms "200" which occur* up to n-1 (* e.g., at n = 256, 511, 766, 1277, 1532, ...). - M. F. Hasler, Aug 09 2018
EXAMPLE
The first suffix block or "glue string" of length 10 is "4454444455", occurring as A091799(5760309077..5760309086). This is also the first occurrence of "55" in A091799. The first suffix block of length 42 is "4454444455"."444445"^5."55" (where . is concatenation) which occurs approximately at position 4.56*10^38. This is also the first occurrence of "555" in A091799. - M. F. Hasler, Aug 08 2018, corrected Sep 30 2018
PROG
(PARI) print_A091842(LIM=oo, A=[], c=#A)={while(#A<LIM, my(k=3, L=0, m=k); while((k+1)*(L+1)<=#A, for(N=L+1, #A/(m+1), A[-m*N..-1]==A[-(m+1)*N..-N-1]&&(m+=1)&&break); m>k||break; k=m); A=concat(A, max(k, 4)); if(k<4, #A>1&&print1(#A-c", "); c=#A))} \\ M. F. Hasler, Aug 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 10 2004
STATUS
approved