A060846 Smallest prime > the n-th nontrivial power of a prime.

5, 11, 11, 17, 29, 29, 37, 53, 67, 83, 127, 127, 131, 173, 251, 257, 293, 347, 367, 521, 541, 631, 733, 853, 967, 1031, 1361, 1373, 1693, 1861, 2053, 2203, 2203, 2213, 2411, 2819, 3137, 3491, 3727, 4099, 4493, 4919, 5051, 5333, 6247, 6563, 6863, 6899, 7927

Offset: 1

Author

Labos Elemer, May 03 2001

Keywords

• nonn

Examples

			78125=5^7 is followed by 78137.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025475, A000961, A001597, A001694, A007917, A007918, A013632, A013633, A049711, A060845, A068435, A246547.

Programs

Mathematica

NextPrime[Select[Range[10^4], !PrimeQ[#] && PrimePowerQ[#] &]] (* Amiram Eldar, Oct 04 2024 *)

PARI

ispp(x) = !isprime(x) && isprimepower(x);
lista(nn) = apply(x->nextprime(x), select(x->ispp(x), [1..nn])); \\ Michel Marcus, Aug 24 2019

Python

from sympy import primepi, integer_nthroot, nextprime
def A060846(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return int(n+x-sum(primepi(integer_nthroot(x,k)[0]) for k in range(2,x.bit_length())))
    return nextprime(bisection(f,n,n)) # Chai Wah Wu, Sep 15 2024

Formula

a(n) = nextprime(A025475(n+1)) = A007918(A025475(n+1)) = Min{p| p>A025475(n+1)}. [corrected by Michel Marcus, Aug 24 2019]