A357385 - OEIS

A357385

a(n) = A071626(n+1) - A071626(n).

1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

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OFFSET

COMMENTS

Conjectures:

1) The only distinct terms of this sequence are -1, 0 and 1.

2) The asymptotic density of the occurrences of 0 is 0.943..., and the asymptotic densities of the occurrences of -1 and 1 are equal and the common value is 0.028... .

These conjectures are empirically supported by the following numbers of occurrences of the terms -1, 0 and 1 up to n = 10^k:

k -1 0 1

- ------- ------- ------

1 0 6 4

2 1 87 12

3 28 913 59

4 362 9189 449

5 3159 93430 3411

6 27853 943571 28576

7 281802 9434309 283889

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000