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A282304 a(n)=least k>0 such that A282291(n+k)<>A282291(n)*A282291(k+1). 2
1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,7

COMMENTS

The sequence can be interpreted like this: for any n>1, the b(n) terms of A282291 starting at index n equal the first b(n) terms of A282291, up to a scaling factor of A282291(n).

Huge values in this sequence accounts for the fractal nature of A282291.

The first records in this sequence are:

n       a(n)    A282291(n)

------  ------  ----------

2            1   2

8            5   5

14          11   7

34          31  11

96          90  13

193        185  17

386        383  19

770        767  23

1538      1535  29

3074      3071  31

14647    11105  37

30533    29455  41

60824    30062  43

122349   91331  47

245225  121951  53

688293  367238  59

The occurrence of a prime number greater that 3 in A282291 seems to settle a new record in this sequence.

This sequence has a similar fractal nature as A282291; yet here, repeated portions are identical (not scaled).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 2..50000

MATHEMATICA

a = {1}; Do[k = 1; While[Or[MemberQ[a, k], Nand[Divisible[#2, #1], CoprimeQ[#1, #2/#1]]] & @@ Sort@ # &@ {k, Last@ a}, k++]; AppendTo[a, k], {n, 300}]; Table[k = 1; While[a[[n + k]] == a[[n]] a[[k + 1]], k++]; k, {n, 2, 120}] (* Michael De Vlieger, Feb 12 2017 *)

CROSSREFS

Cf. A282291.

Sequence in context: A344757 A046623 A046602 * A250662 A340366 A031261

Adjacent sequences:  A282301 A282302 A282303 * A282305 A282306 A282307

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Feb 11 2017

STATUS

approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)