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A373179
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a(n) is the smallest n-digit integer whose digit permutations make the maximum possible number of n-digit primes.
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1
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2, 13, 149, 1237, 13789, 123479, 1235789, 12345679, 102345679, 1123456789, 10123456789, 1011233456789, 1012334567789, 10123345677899
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OFFSET
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1,1
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COMMENTS
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A065851(n) is the maximum number of n-digit primes which can be made by permuting n digits.
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).
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LINKS
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EXAMPLE
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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.)
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PROG
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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
(C) /* See links. */
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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