A323065 -id:A323065 - cp's OEIS frontend

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

Simon Plouffe, Feb 06 2019

nonn

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

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.

Cf. A323176, A323065, A323611.

# 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;

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

A323611 Prime numbers generated by the formula a(n) = round(c(n)), where c(n) = c(n-1)^(3/2) for n >= 2 starting with c(1) = C and C the real constant given below.

Original entry on oeis.org

2, 3, 5, 11, 37, 223, 3331, 192271, 84308429, 774116799347, 681098209317971743, 562101323304225290104514179, 13326678220145859782825116625722145759009, 1538448162271607869601834587431948506238982765193425993274489

Offset: 1

Simon Plouffe, Jan 20 2019

nonn

C = 2.038239154782068767463490862609548251448624778443173613879675732.

			c(1) = 2.038239154782068, c(2) = 2.9099311279, c(3) = 4.96391190457, c(4) = 11.05951540, ... so a(1) = {c(1)} = 2, a(2) = {c(2)} = 3, a(3) = {c(3)} = 5, ...
c(n) = c(n-1)^(3/2) and a(n) = {c(n)} is the value rounded to the nearest integer.

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

Cf. A323176, A323065.

# Computes the values according to the formula, c = 2.03823915478..., e = 3/2, m the number of terms. Returns the real and the rounded values (primes).
val := proc(c, e, m)
local ll, v, n;
    v := c;
    ll := [v];
    for n to m-1 do
        v := v^e; ll := [op(ll), v]
    end do;
    return [ll, map(round, ll)]
end:

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Formula