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

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

Offset: 2

Author

Rémy Sigrist, Feb 11 2017

Keywords

• nonn

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).

The presence of 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 than 3 in A282291 seems to set 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

Crossrefs

Cf. A282291.

Programs

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 *)