FORMULA FOR A283623: a(n) = prime(n) + (1 + prime(1 + n))/2.

[Davide Rotondo]

Happy new year dear seq fans. Today I think I found a 

FORMULA FOR A283623:
a(n) = prime(n) + (1 + prime(1 + n))/2.

4, 6, 9, 13, 18, 22, 27, 31, 38, 45, 50, 58, 63, ...

EXAMPLE
a(1) = 2 + (1 + 3)/2 = 4,
a(2) = 3 + (1 + 5)/2 = 6,
a(3) = 5 + (1 + 7)/2 = 9.

METHOD
Using the constant A249270
Decimal expansion of lim_{n->oo} (1/n)*Sum_{k=1..n} smallest prime not dividing k: 2.9200509773161347120925629171120194680027278993214267...

The ceil integer parts of the sequence having this constant as starting value and thereafter x[n+1] = (frac(x[n])+1)*floor(p[n]) where p are the prime numbers >=3.

Example
ceil(3(2.9200509773161347120925629171120194680027278993214267-2+1)) = 6

What do you think?

Is this interesting?

Davide

[Ruud H.G. van Tol]

That formula is already the name of the sequence. Probably good to put
it in the Formula-section as well.

Your other observations could go in the comments, or into a linked file.

-- Ruud