

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
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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 SlowGrowing 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(n1,4)) for n < 259. For larger n, the index n must be increased by the number of terms "200" which occur* up to n1 (* 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..N1]&&(m+=1)&&break); m>kbreak; k=m); A=concat(A, max(k, 4)); if(k<4, #A>1&&print1(#Ac", "); 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



