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A282304 a(n) is the least k > 0 such that A282291(n+k) != A282291(n) * A282291(k+1).

%I A282304 #15 Aug 30 2021 21:55:00
%S A282304 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 A282304 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 A282304 1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,2,1
%N A282304 a(n) is the least k > 0 such that A282291(n+k) != A282291(n) * A282291(k+1).
%C A282304 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 A282304 The presence of huge values in this sequence accounts for the fractal nature of A282291.
%C A282304 The first records in this sequence are:
%C A282304        n    a(n)  A282291(n)
%C A282304   ------  ------  ----------
%C A282304        2       1       2
%C A282304        8       5       5
%C A282304       14      11       7
%C A282304       34      31      11
%C A282304       96      90      13
%C A282304      193     185      17
%C A282304      386     383      19
%C A282304      770     767      23
%C A282304     1538    1535      29
%C A282304     3074    3071      31
%C A282304    14647   11105      37
%C A282304    30533   29455      41
%C A282304    60824   30062      43
%C A282304   122349   91331      47
%C A282304   245225  121951      53
%C A282304   688293  367238      59
%C A282304 The occurrence of a prime number greater than 3 in A282291 seems to set a new record in this sequence.
%C A282304 This sequence has a similar fractal nature as A282291; yet here, repeated portions are identical (not scaled).
%H A282304 Rémy Sigrist, <a href="/A282304/b282304.txt">Table of n, a(n) for n = 2..50000</a>
%t A282304 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 A282304 Cf. A282291.
%K A282304 nonn
%O A282304 2,7
%A A282304 _Rémy Sigrist_, Feb 11 2017