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A087633 Number of n-digit primes ending in 9 in base 10. 4
0, 5, 33, 265, 2087, 17203, 146439, 1274154, 11271147, 101049993, 915748570, 8372464236, 77114396969 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..13.

FORMULA

From Iain Fox, Aug 07 2018: (Start)

a(n) ~ (1/4) * Integral_{x=10^(n-1)..10^n} (dx/log(x)).

a(n) = A006879(n) - A087630(n) - A087631(n) - A087632(n), for n > 1.

(End)

EXAMPLE

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.

MATHEMATICA

Table[Length[Select[Range[10^n + 9, 10^(n + 1) - 1, 10], PrimeQ]], {n, 5}] (* Alonso del Arte, Apr 27 2014 *)

PROG

(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

CROSSREFS

Cf. A006879, A073508, A087630, A087631, A087632.

Sequence in context: A199552 A061253 A111530 * A135075 A269820 A302075

Adjacent sequences:  A087630 A087631 A087632 * A087634 A087635 A087636

KEYWORD

nonn,base,hard,more

AUTHOR

Meenakshi Srikanth (menakan_s(AT)yahoo.com) and Amarnath Murthy, Sep 15 2003

EXTENSIONS

Corrected and extended by Ray Chandler, Oct 04 2003

Offset corrected by Iain Fox, Aug 07 2018

a(11) from Iain Fox, Aug 07 2018

a(12)-a(13) from Giovanni Resta, Aug 07 2018

STATUS

approved

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Last modified May 13 06:11 EDT 2021. Contains 343836 sequences. (Running on oeis4.)