A373179 a(n) is the smallest n-digit integer whose digit permutations make the maximum possible number of n-digit primes.
2, 13, 149, 1237, 13789, 123479, 1235789, 12345679, 102345679, 1123456789, 10123456789, 1011233456789, 1012334567789, 10123345677899
Offset: 1
Examples
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.)
Links
- Kevin Ryde, C Code
Programs
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C
/* See links. */
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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), key=lambda x:smallest(x[0])) return smallest(m[0]) # m[1] generates A065851 print([a(n) for n in range(1, 8)]) # Michael S. Branicky, May 28 2024
Extensions
a(9)-a(11) from Michael S. Branicky, May 27 2024
a(12)-a(14) from Kevin Ryde, Jul 16 2024
Comments