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A098224
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Number of primes <=10^n in which decimal digits are all distinct.
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5
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4, 24, 121, 631, 3160, 13399, 47349, 137859, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086
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OFFSET
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1,1
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COMMENTS
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No number with more than 10 digits can have all of its decimal digits distinct, and no number that uses all ten distinct decimal digits can be prime (because the sum of all ten decimal digits is 45 so any such number is divisible by 3). Therefore, every term in the sequence from and after a(9) is the same, i.e., 283086. - Harvey P. Dale, Dec 12 2010
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LINKS
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FORMULA
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a(n) = 283086 for n >= 9.
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MATHEMATICA
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okQ[n_]:=Max[DigitCount[n]]==1
Table[Length[Select[Prime[Range[PrimePi[10^i]]], okQ]], {i, 9}] (* Harvey P. Dale, Dec 12 2010 *)
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PROG
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(Python)
from sympy import sieve
def distinct_digs(n): s = str(n); return len(s) == len(set(s))
def aupton(terms):
ps, alst = 0, []
for n in range(1, terms+1):
if n >= 10: alst.append(ps); continue
ps += sum(distinct_digs(p) for p in sieve.primerange(10**(n-1), 10**n))
alst.append(ps)
return alst
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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