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A266148
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Number of n-digit primes in which n-1 of the digits are 9's.
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11
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4, 6, 7, 7, 8, 10, 7, 13, 8, 8, 11, 13, 8, 11, 13, 14, 10, 9, 7, 11, 9, 13, 10, 19, 5, 10, 14, 7, 10, 9, 9, 15, 13, 8, 7, 9, 10, 11, 10, 13, 5, 12, 15, 7, 12, 7, 12, 11, 13, 11, 8, 13, 13, 13, 12, 12, 9, 9, 15, 14, 9, 8, 13, 11, 15, 17, 10, 8, 11, 10, 6, 16, 8, 8, 8, 15, 9, 11, 14, 7, 10, 11, 16, 17, 11, 10, 12, 16, 8, 15, 7, 11, 11, 10, 7, 12, 6, 10, 8, 9
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OFFSET
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1,1
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COMMENTS
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The other digit cannot be 0, 3, 6, or 9, or else the number would not be prime. - N. J. A. Sloane, May 20 2016
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LINKS
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EXAMPLE
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a(3) = 7 since 199, 499, 599, 919, 929, 991 and 997 are all the three-digit primes containing two 9's.
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MATHEMATICA
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f9[n_] := Block[{cnt = k = 0, r = 9 (10^n - 1)/9, s = Range[0, 9] - 9}, While[k < n, cnt += Length@ Select[r + 10^k * s, PrimeQ@ # && IntegerLength@ # > k &]; k++]; cnt]; Array[f9, 100]
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PROG
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(Python)
from sympy import isprime
return sum(1 for d in range(-9, 1) for i in range(n) if isprime(10**n-1+d*10**i)) # Chai Wah Wu, Dec 31 2015
(Perl) use ntheory ":all"; sub a266148 { my $n = shift; vecsum( map { my $k=$_; scalar grep { is_prime("9" x $k . $_ . "9" x ($n-$k-1)) } 0+($k>0) .. 8 } 0 .. $n-1 ); } # Dana Jacobsen, Jan 01 2016
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CROSSREFS
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Cf. A265733, A266141, A266142, A266143, A266144, A266145, A266146, A266147, A266149, A095714, A089675.
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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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