A323065 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.

3, 5, 7, 11, 19, 41, 103, 331, 1423, 8819, 86477, 1504949, 53691233, 4703173021, 1267699542037, 1394588856899951, 8916055416478425247

Offset: 1

Author

Simon Plouffe, Jan 20 2019

Keywords

• nonn
• more

Comments

C = 3.346835535932430816866371614510056305833213572055338155233562507

and exponent

d = 1.251295195638613270470338478487766898374146819139632632235793814.

Examples

			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.
		

Links

• Simon Plouffe, A set of formulas for primes, arXiv:1901.01849 [math.NT], 2019.

Crossrefs

Cf. A323176.

Programs

Maple

# 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).
val := proc(s, d, m)
local ll, v, n;
    v := s;
    ll := [v];
    for n to m-1 do
        v := v^d; ll := [op(ll), v]
    end do;
    return [ll, map(round, ll)]
end: