A323611 Prime numbers generated by the formula a(n) = round(c(n)), where c(n) = c(n-1)^(3/2) for n >= 2 starting with c(1) = C and C the real constant given below.

2, 3, 5, 11, 37, 223, 3331, 192271, 84308429, 774116799347, 681098209317971743, 562101323304225290104514179, 13326678220145859782825116625722145759009, 1538448162271607869601834587431948506238982765193425993274489

Offset

1,1

Comments

C = 2.038239154782068767463490862609548251448624778443173613879675732.

Links

Table of n, a(n) for n=1..14.

Simon Plouffe, A set of formulas for primes, arXiv:1901.01849 [math.NT], 2019.

Example

c(1) = 2.038239154782068, c(2) = 2.9099311279, c(3) = 4.96391190457, c(4) = 11.05951540, ... so a(1) = {c(1)} = 2, a(2) = {c(2)} = 3, a(3) = {c(3)} = 5, ...
c(n) = c(n-1)^(3/2) and a(n) = {c(n)} is the value rounded to the nearest integer.

Maple

# Computes the values according to the formula, c = 2.03823915478..., e = 3/2, m the number of terms. Returns the real and the rounded values (primes).
val := proc(c, e, m)
local ll, v, n;
    v := c;
    ll := [v];
    for n to m-1 do
        v := v^e; ll := [op(ll), v]
    end do;
    return [ll, map(round, ll)]
end:

Crossrefs

Cf. A323176, A323065.

Sequence in context: A111289 A255420 A127181 * A113734 A222007 A188142

Adjacent sequences: A323608 A323609 A323610 * A323612 A323613 A323614

Keyword

nonn

Author

Simon Plouffe, Jan 20 2019

Status

approved