|
| |
|
|
A087631
|
|
Number of n-digit primes ending in 3 in base 10.
|
|
4
|
|
|
|
1, 6, 35, 268, 2092, 17263, 146565, 1274244, 11272025, 101053126, 915743823, 8372470456, 77114448042
(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) - A087632(n) - A087633(n), for n > 1.
(End)
|
|
|
EXAMPLE
|
a(2) = 6, as there exist 6 two-digit prime numbers (13, 23, 43, 53, 73, and 83) with units place 3.
a(3) = 35, since there are 35 three-digit numbers with units place digit as 3.
|
|
|
MATHEMATICA
|
Table[Length[Select[Range[10^n + 3, 10^(n + 1) - 7, 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 == 3) 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==3, c++)); c \\ Iain Fox, Aug 07 2018
|
|
|
CROSSREFS
|
Cf. A006879, A073506, A087630, A087632, A087633.
Sequence in context: A244267 A187443 A325115 * A167579 A357095 A030446
Adjacent sequences: A087628 A087629 A087630 * A087632 A087633 A087634
|
|
|
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
|
| |
|
|
