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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 (list; graph; refs; listen; history; text; internal format)
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

M. F. Hasler, Table of n, a(n) for n = 1..1500

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.

Index entries for sequences related to Gijswijt's sequence

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

Cf. A091787, A090822, A091579, A091840, A091843, A091799.

Sequence in context: A176563 A093148 A069292 * A306346 A060901 A087612

Adjacent sequences:  A091839 A091840 A091841 * A091843 A091844 A091845

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 10 2004

STATUS

approved

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Last modified June 24 18:25 EDT 2019. Contains 324330 sequences. (Running on oeis4.)