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A323065 Prime numbers generated by the formula a(n) = round(c(n)), where c(n) = c(n-1)^d for n >= 2 starting with c(1) = C. C and d are the real constants given below.

%I A323065 #58 Jan 22 2019 04:51:43
%S A323065 3,5,7,11,19,41,103,331,1423,8819,86477,1504949,53691233,4703173021,
%T A323065 1267699542037,1394588856899951,8916055416478425247
%N A323065 Prime numbers generated by the formula a(n) = round(c(n)), where c(n) = c(n-1)^d for n >= 2 starting with c(1) = C. C and d are the real constants given below.
%C A323065 C = 3.346835535932430816866371614510056305833213572055338155233562507
%C A323065 and exponent
%C A323065 d = 1.251295195638613270470338478487766898374146819139632632235793814.
%H A323065 Simon Plouffe, <a href="https://arxiv.org/abs/1901.01849">A set of formulas for primes</a>, arXiv:1901.01849 [math.NT], 2019.
%e A323065 c(1) = 3.3468, a(1) = 3; c(2) = 4.53390554, a(2) = 5; c(3) = 6.6288905, a(3) = 7; ...; c(n) = c(n-1)^d and a(n) = {c(n)} is the value rounded to the nearest integer.
%p A323065 # Computes the values according to the formula, s = 3.34683553..., d = 1.2512951, m the number of terms. Returns the real and the rounded values (primes).
%p A323065 val := proc(s, d, m)
%p A323065 local ll, v, n;
%p A323065     v := s;
%p A323065     ll := [v];
%p A323065     for n to m-1 do
%p A323065         v := v^d; ll := [op(ll), v]
%p A323065     end do;
%p A323065     return [ll, map(round, ll)]
%p A323065 end:
%Y A323065 Cf. A323176.
%K A323065 nonn,more
%O A323065 1,1
%A A323065 _Simon Plouffe_, Jan 20 2019