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A087632 Number of n-digit primes ending in 7 in base 10. 4
1, 5, 40, 262, 2103, 17210, 146590, 1274284, 11271819, 101051725, 915754298, 8372478663, 77114370790 (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) - A087633(n), for n > 1.

(End)

EXAMPLE

a(2) = 5 as there exist 5 two-digit prime numbers (17, 37, 47, 67, and 97) with units place 7.

a(3) = 40, since there are 40 three-digit numbers with units place digit as 7.

MATHEMATICA

Table[Length[Select[Range[10^n + 7, 10^(n + 1) - 3, 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 == 7) 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==7, c++)); c \\ Iain Fox, Aug 07 2018

CROSSREFS

Cf. A006879, A073507, A087630, A087631, A087633.

Sequence in context: A054604 A157794 A001656 * A229279 A124306 A124545

Adjacent sequences:  A087629 A087630 A087631 * A087633 A087634 A087635

KEYWORD

nonn,base,hard,more

AUTHOR

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

EXTENSIONS

More terms from 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 October 17 11:26 EDT 2019. Contains 328108 sequences. (Running on oeis4.)