A294148 a(n) is the smallest prime whose square is greater than the cube of a(n-1); a(1) = 2.

2, 3, 7, 19, 83, 757, 20849, 3010457, 5223344167, 377505222176491, 7334735304307198091659, 628169243329433959747511898881729, 15743997159315671181189678367886578609038417676391, 62470143575895304690094463208359121879929322420894118855801094477279900397

Offset

1,1

Comments

a(n) is the smallest prime such that a(n) > a(n-1)^(3/2); a(1) = 2.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..20

Example

a(2) = 3 because 3^2 = 9 > a(1)^3 = 8 and 3 is the smallest such prime.
a(3) = 7 because 7^2 = 49 > a(2)^3 = 27 and 7 is the smallest such prime.

Mathematica

f[s_List] := Append[s, NextPrime[ Sqrt[s[[-1]]^3]]]; s = {2}; Nest[f, s, 13] (* Robert G. Wilson v, Nov 18 2017 *)

Prog

(PARI) {
p=2; print1(p", ");
for(n=1, 10,
    p1=nextprime(p+1);
    while(p^3>p1^2, p1=nextprime(p1+1));
    p=p1; print1(p1", ")
   )
}
(PARI) lista(nn) = {a=2; print1(a, ", "); for (n=1, nn, a=nextprime(sqrtint(a^3)+1); print1(a, ", ")); } \\ Michel Marcus, Oct 29 2017

Crossrefs

Cf. A001248 and A030078 (squares and cubes of primes).

Cf. A059842 (similar, with n instead of prime(n)).

Sequence in context: A110887 A065060 A164625 * A079804 A325057 A075487

Adjacent sequences: A294145 A294146 A294147 * A294149 A294150 A294151

Keyword

nonn

Author

Dimitris Valianatos, Oct 23 2017

Extensions

a(10)-a(14) from Michel Marcus, Oct 29 2017

Status

approved