

A087630


Number of ndigit primes ending in 1 in base 10.


4



0, 5, 35, 266, 2081, 17230, 146487, 1274194, 11271088, 101050133, 915755611, 8372443850, 77114409020
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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^(n1)..10^n} (dx/log(x)).
a(n) = A006879(n)  A087631(n)  A087632(n)  A087633(n), for n > 1.
(End)


EXAMPLE

a(2) = 5 as there exist 5 twodigit prime numbers (11, 31, 41, 61, and 71) with units place 1.
a(3) = 35, since there are 35 threedigit numbers with units place digit as 1.


MATHEMATICA

Table[Length[Select[Range[10^n + 1, 10^(n + 1)  9, 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 threedigit 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 == 1) count = count + 1; } c = 0; } System.out.println("count = " + count);
(PARI) a(n) = my(c=0); forprime(p=10^(n1), 10^n, if(p%10==1, c++)); c \\ Iain Fox, Aug 07 2018


CROSSREFS

Cf. A006879, A073505, A087631, A087632, A087633.
Sequence in context: A104532 A292839 A180900 * A084135 A229111 A138233
Adjacent sequences: A087627 A087628 A087629 * A087631 A087632 A087633


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



