A306317 - OEIS

%I #30 Mar 16 2019 12:25:02

%S 2,3,5,7,13,29,79,293,1619,14947,269237,11570443,1540936027,

%T 893681319109,3513374197622981,166491395148719076277,

%U 201072926144898161374940903,16390008340104365722976984827792343,320076519482444467256811692239892862140322229,7781106039755041703318535124896118983796534882794414187099

%N Prime numbers generated by the formula a(n) = round(2^(d^n)), where d is the real constant 1.30076870414817691055252567828266106688423996320151467218595488...

%C The exponent d = 1.3007687... is the smallest found.

%H Simon Plouffe, <a href="/A306317/b306317.txt">Table of n, a(n) for n = 1..24</a>

%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="http://vixra.org/abs/1902.0036">Une formule pour les nombres premiers</a>, viXra:1902.0036.

%F a(n) = round(2^(d^n)), where d is a real constant starting 1.30076870414817691055252567828266106688423996320151467218595488...

%p # Computes the values according to the formula, v = 2..., e = 1.30076870414817691055252567828266106688423996320151467218595488..., m the # number of terms. Returns the real and the rounded values (primes). In this case 23 terms will be generated

%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;

%Y Cf. A323176, A323065, A323611.

%K nonn

%O 1,1

%A _Simon Plouffe_, Feb 06 2019