%I #40 Jul 16 2024 15:55:09

%S 2,13,149,1237,13789,123479,1235789,12345679,102345679,1123456789,

%T 10123456789,1011233456789,1012334567789,10123345677899

%N a(n) is the smallest n-digit integer whose digit permutations make the maximum possible number of n-digit primes.

%C A065851(n) is the maximum number of n-digit primes which can be made by permuting n digits.

%C a(n) = k is the smallest n-digit k for which A046810(k) = A065851(n).

%C a(n) has its 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).

%H Kevin Ryde, <a href="/A065851/a065851.c.txt">C Code</a>

%e 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.)

%o (Python)

%o from sympy import nextprime

%o from collections import Counter

%o def smallest(t):

%o nz = "".join(sorted(c for c in t if c != "0"))

%o s = "".join(t) if "0" not in t else nz[0]+"0"*t.count("0")+nz[1:]

%o return int(s)

%o def a(n):

%o c, p = Counter(), nextprime(10**(n-1))

%o while p < 10**n:

%o c["".join(sorted(str(p)))] += 1

%o p = nextprime(p)

%o m = min(c.most_common(1), key=lambda x:smallest(x[0]))

%o return smallest(m[0]) # m[1] generates A065851

%o print([a(n) for n in range(1, 8)]) # _Michael S. Branicky_, May 28 2024

%o (C) /* See links. */

%Y Cf. A000040, A046810, A065851, A134596, A179239.

%K nonn,base,more

%O 1,1

%A _Gonzalo Martínez_, May 26 2024

%E a(9)-a(11) from _Michael S. Branicky_, May 27 2024

%E a(12)-a(14) from _Kevin Ryde_, Jul 16 2024