A282304 - OEIS

%I #15 Aug 30 2021 21:55:00

%S 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,

%T 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,

%U 1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,2,1

%N a(n) is the least k > 0 such that A282291(n+k) != A282291(n) * A282291(k+1).

%C 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).

%C The presence of huge values in this sequence accounts for the fractal nature of A282291.

%C The first records in this sequence are:

%C        n    a(n)  A282291(n)

%C   ------  ------  ----------

%C        2       1       2

%C        8       5       5

%C       14      11       7

%C       34      31      11

%C       96      90      13

%C      193     185      17

%C      386     383      19

%C      770     767      23

%C     1538    1535      29

%C     3074    3071      31

%C    14647   11105      37

%C    30533   29455      41

%C    60824   30062      43

%C   122349   91331      47

%C   245225  121951      53

%C   688293  367238      59

%C The occurrence of a prime number greater than 3 in A282291 seems to set a new record in this sequence.

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

%H Rémy Sigrist, <a href="/A282304/b282304.txt">Table of n, a(n) for n = 2..50000</a>

%t 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 *)

%Y Cf. A282291.

%K nonn

%O 2,7

%A _Rémy Sigrist_, Feb 11 2017