A306317 Prime numbers generated by the formula a(n) = round(2^(d^n)), where d is the real constant 1.30076870414817691055252567828266106688423996320151467218595488...

2, 3, 5, 7, 13, 29, 79, 293, 1619, 14947, 269237, 11570443, 1540936027, 893681319109, 3513374197622981, 166491395148719076277, 201072926144898161374940903, 16390008340104365722976984827792343, 320076519482444467256811692239892862140322229, 7781106039755041703318535124896118983796534882794414187099

Offset: 1

Author

Simon Plouffe, Feb 06 2019

Keywords

• nonn

Comments

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

Links

• Simon Plouffe, Table of n, a(n) for n = 1..24
• Simon Plouffe, A set of formulas for primes, arXiv:1901.01849 [math.NT], 2019.
• Simon Plouffe, Une formule pour les nombres premiers, viXra:1902.0036.

Crossrefs

Cf. A323176, A323065, A323611.

Programs

Maple

# 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
val := proc(s, e, m)
local ll, v, n, kk;
    v := s;
    ll := [];
    for n to m do
        v := v^e; ll := [op(ll), v]
    end do;
    return [ll, map(round, ll)]
end;

Formula

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