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A266148 Number of n-digit primes in which n-1 of the digits are 9's. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
Dana Jacobsen, Table of n, a(n) for n = 1..2500 (first 1215 terms from Michael De Vlieger and Robert G. Wilson v)
EXAMPLE
a(3) = 7 since 199, 499, 599, 919, 929, 991 and 997 are all the three-digit primes containing two 9's.
MATHEMATICA
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]
PROG
(Python)
from sympy import isprime
def A266148(n):
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
CROSSREFS
Sequence in context: A198882 A366727 A000703 * A011275 A205684 A006185
KEYWORD
base,nonn
AUTHOR
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)