A323065 - OEIS

%I #58 Jan 22 2019 04:51:43

%S 3,5,7,11,19,41,103,331,1423,8819,86477,1504949,53691233,4703173021,

%T 1267699542037,1394588856899951,8916055416478425247

%N 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 C = 3.346835535932430816866371614510056305833213572055338155233562507

%C and exponent

%C d = 1.251295195638613270470338478487766898374146819139632632235793814.

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

%e 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 # 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 val := proc(s, d, m)

%p local ll, v, n;

%p     v := s;

%p     ll := [v];

%p     for n to m-1 do

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

%p     end do;

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

%p end:

%Y Cf. A323176.

%K nonn,more

%O 1,1

%A _Simon Plouffe_, Jan 20 2019