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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.

%I A323611 #33 Jan 22 2019 04:51:38
%S A323611 2,3,5,11,37,223,3331,192271,84308429,774116799347,681098209317971743,
%T A323611 562101323304225290104514179,
%U A323611 13326678220145859782825116625722145759009,1538448162271607869601834587431948506238982765193425993274489
%N 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.
%C A323611 C = 2.038239154782068767463490862609548251448624778443173613879675732.
%H A323611 Simon Plouffe, <a href="https://arxiv.org/abs/1901.01849">A set of formulas for primes</a>, arXiv:1901.01849 [math.NT], 2019.
%e A323611 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, ...
%e A323611 c(n) = c(n-1)^(3/2) and a(n) = {c(n)} is the value rounded to the nearest integer.
%p A323611 # 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).
%p A323611 val := proc(c, e, m)
%p A323611 local ll, v, n;
%p A323611     v := c;
%p A323611     ll := [v];
%p A323611     for n to m-1 do
%p A323611         v := v^e; ll := [op(ll), v]
%p A323611     end do;
%p A323611     return [ll, map(round, ll)]
%p A323611 end:
%Y A323611 Cf. A323176, A323065.
%K A323611 nonn
%O A323611 1,1
%A A323611 _Simon Plouffe_, Jan 20 2019