A323176 - OEIS

%I #27 May 26 2020 18:08:09

%S 113,367,1607,10177,102217,1827697,67201679,6084503671,1699344564793,

%T 1940223714629437,12877001925259260821,771380135526168946568519,

%U 722912215706743477640066820689,21079337353575904691781436731789131951,45166994522409258021988187061430676460306223027,20822194129240450122637347266336444580153717439156314146339

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

%C The constant c is given in the article [Plouffe, 2018] with 2600 digits of precision.

%H Simon Plouffe, <a href="https://arxiv.org/abs/1901.01849">A set of formulas for primes</a>, arXiv:1901.01849 [math.NT], 2019.

%H 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 a(n) = round(c^((5/4)^n)), where c is a real constant starting 43.80468771580293481859664562569089495081037087137495184074061328752670419506...

%e a(1) = round(c^((5/4)^1)) = round(112.69...) =  113,

%e a(2) = round(c^((5/4)^2)) = round(367.17...) =  367,

%e a(3) = round(c^((5/4)^3)) = round(1607.2...) = 1607, etc..

%p # Computes the values according to the formula, v = 43.804..., e = 5/4, m the

%p # number of terms. Returns the real and the rounded values (primes).

%p val := proc(s, e, m)

%p local ll, v, n, kk;

%p     v := s;

%p     ll := [];

%p     for n to m do

%p         v := v^e; ll := [op(ll), v]

%p     end do;

%p     return [ll, map(round, ll)]

%p end;

%K nonn

%O 1,1

%A _Simon Plouffe_, Jan 05 2019