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A087633
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Number of n-digit primes ending in 9 in base 10.
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4
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0, 5, 33, 265, 2087, 17203, 146439, 1274154, 11271147, 101049993, 915748570, 8372464236, 77114396969
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) ~ (1/4) * Integral_{x=10^(n-1)..10^n} (dx/log(x)).
(End)
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EXAMPLE
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a(2) = 5 as there exist 5 two-digit prime numbers (19, 29, 59, 79, and 89) with units place 9.
a(3) = 33, since there are 33 three-digit numbers with units place digit as 9.
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MATHEMATICA
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Table[Length[Select[Range[10^n + 9, 10^(n + 1) - 1, 10], PrimeQ]], {n, 5}] (* Alonso del Arte, Apr 27 2014 *)
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PROG
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(Java) /** The terms of the sequences are generated by changing the range for j for the various numbers of digits. E.g., it ranges from 100 to 999 for three-digit numbers. */
float r, x;
int c = 0, count = 0; for (float j = 100f; j < 1000f; j++) { for (float i = 2f; i < j; i++) { r = j % i; if (r == 0) c = 1; } if (c == 0) { x = j % 10; if (x == 9) count = count + 1; } c = 0; } System.out.println("count = " + count);
(PARI) a(n) = my(c=0); forprime(p=10^(n-1), 10^n, if(p%10==9, c++)); c \\ Iain Fox, Aug 07 2018
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CROSSREFS
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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Meenakshi Srikanth (menakan_s(AT)yahoo.com) and Amarnath Murthy, Sep 15 2003
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EXTENSIONS
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Offset corrected by Iain Fox, Aug 07 2018
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STATUS
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approved
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