# prime sequence

Thu Feb 17 10:18:29 CET 2005

```    Neil

These are some prime related sequences.
Are they fit to OEIS?
If so, I will format them.

%S A000001     2, 1, 2, 1, 5, 3, 8, 4, 3, 14
%N A000001    [Prime(n)/(Prime(n+1)-Prime(n))]

This is reciprocal number of a distance between adjacent primes

%S A000002    0, -1, 1, -1, 1, -1, -1, 2, -2,
%N A000002    Prime(n)-(Prime(n+1)+Prime(n-1))/2
OffSet 5

I think that it represents a distance of Prime(n) and linear sequence.
I awoke that it is -1/2*{the difference of A001223}

%S A000003    0, 1, 2, 1, 2, 2, 4, 3, 2, 2, 1,
%N A000003    f(m)=(m+1)/2^r , a(n)={minimal k such that f^k
(Prime(n))=1}
f(f(f(f(17))))=1 , so a(17)=4

%S A000004    2, 1, 3, 2, 1, 1, 3, 1, 5, 1,
%N A000004    2^a(n) is the largest power of two dividing (Prime(n)+1)

It appears when we use P+1 prime test.

Yasutoshi

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