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A266146
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Number of n-digit primes in which n-1 of the digits are 7's.
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11
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4, 8, 10, 9, 12, 11, 8, 4, 9, 9, 10, 14, 14, 11, 16, 7, 10, 17, 7, 10, 9, 12, 9, 13, 11, 10, 14, 5, 3, 22, 6, 13, 13, 10, 8, 16, 8, 6, 16, 8, 13, 14, 8, 7, 8, 13, 9, 11, 13, 9, 14, 8, 4, 23, 13, 11, 8, 8, 8, 12, 13, 13, 11, 11, 10, 23, 11, 8, 8, 3, 6, 16, 12, 13, 12, 12, 8, 11, 8, 11, 14, 13, 7, 15, 12, 17, 11, 7, 9, 21, 6, 6, 11, 12, 6, 14, 14, 12, 13, 12, 11, 17, 10, 17, 18
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(2) = 8 from 17, 37, 47, 67, 71, 73, 79, 97. - N. J. A. Sloane, Dec 27 2015
a(3) = 10 since 277, 577, 677, 727, 757, 773, 787, 797, 877, and 977 are primes.
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MATHEMATICA
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f7[n_] := Block[{cnt = k = 0, r = 7 (10^n - 1)/9, s = Range[0, 9] - 7}, While[k < n, cnt += Length@ Select[r + 10^k*s, PrimeQ@ # && IntegerLength@ # > k &]; k++]; cnt]; Array[f7, 100]
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PROG
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(PARI) a(n)={sum(i=0, n-1, sum(d=i==n-1, 9, isprime((10^n-1)/9*7 + (d-7)*10^i)))} \\ Andrew Howroyd, Feb 28 2018
(Python)
from __future__ import division
from sympy import isprime
return 4*n if (n==1 or n==2) else sum(1 for d in range(-7, 3) for i in range(n) if isprime(7*(10**n-1)//9+d*10**i)) # Chai Wah Wu, Dec 27 2015
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CROSSREFS
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Cf. A265733, A266141, A266142, A266143, A266144, A266145, A266147, A266148, A266149, A099419, A099420, A098089.
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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