OFFSET
1,1
COMMENTS
A065851(n) is the maximum number of n-digit primes which can be made by permuting n digits, and a(n) is the smallest number which reaches this maximum.
a(n) is the relevant digits sorted and not beginning with 0, and may or may not be one of the primes (it is for n = 1 to 7, but not at n = 8).
EXAMPLE
For n=3, A065851(3) = 4 primes are reached by permuting the digits of a(3) = 149, namely {149, 419, 491, 941}. (4 primes are also reached from 179 and 379, but they're bigger numbers.)
PROG
(Python)
from sympy import nextprime
from collections import Counter
def smallest(t):
nz = "".join(sorted(c for c in t if c != "0"))
s = "".join(t) if "0" not in t else nz[0]+"0"*t.count("0")+nz[1:]
return int(s)
def a(n):
c, p = Counter(), nextprime(10**(n-1))
while p < 10**n:
c["".join(sorted(str(p)))] += 1
p = nextprime(p)
m = min(c.most_common(1))
return smallest(m[0]) # m[1] generates A065851
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, May 28 2024
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Gonzalo MartÃnez, May 26 2024
EXTENSIONS
a(9)-a(11) from Michael S. Branicky, May 27 2024
STATUS
proposed