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A323176 Prime numbers generated by the formula a(n) = round(c^((5/4)^n)), where c is the real constant given below.

%I A323176 #27 May 26 2020 18:08:09
%S A323176 113,367,1607,10177,102217,1827697,67201679,6084503671,1699344564793,
%T A323176 1940223714629437,12877001925259260821,771380135526168946568519,
%U A323176 722912215706743477640066820689,21079337353575904691781436731789131951,45166994522409258021988187061430676460306223027,20822194129240450122637347266336444580153717439156314146339
%N A323176 Prime numbers generated by the formula a(n) = round(c^((5/4)^n)), where c is the real constant given below.
%C A323176 The constant c is given in the article [Plouffe, 2018] with 2600 digits of precision.
%H A323176 Simon Plouffe, <a href="https://arxiv.org/abs/1901.01849">A set of formulas for primes</a>, arXiv:1901.01849 [math.NT], 2019.
%H A323176 Simon Plouffe, <a href="https://arxiv.org/abs/2002.12137">The calculation of p(n) and pi(n)</a>, arXiv:2002.12137 [math.NT], 2020.
%F A323176 a(n) = round(c^((5/4)^n)), where c is a real constant starting 43.80468771580293481859664562569089495081037087137495184074061328752670419506...
%e A323176 a(1) = round(c^((5/4)^1)) = round(112.69...) =  113,
%e A323176 a(2) = round(c^((5/4)^2)) = round(367.17...) =  367,
%e A323176 a(3) = round(c^((5/4)^3)) = round(1607.2...) = 1607, etc..
%p A323176 # Computes the values according to the formula, v = 43.804..., e = 5/4, m the
%p A323176 # number of terms. Returns the real and the rounded values (primes).
%p A323176 val := proc(s, e, m)
%p A323176 local ll, v, n, kk;
%p A323176     v := s;
%p A323176     ll := [];
%p A323176     for n to m do
%p A323176         v := v^e; ll := [op(ll), v]
%p A323176     end do;
%p A323176     return [ll, map(round, ll)]
%p A323176 end;
%K A323176 nonn
%O A323176 1,1
%A A323176 _Simon Plouffe_, Jan 05 2019