A065683 Number of primes <= prime(n) which begin with a 4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20

Offset

1,14

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

41 = A000040(13) is the first prime beginning with 4, so a(13) = 1. a(664579) = 74114 (A000040(664579) = 9999991 is the largest prime < 10^7).

Mathematica

Table[Count[Take[Prime[Range[100]], n], _?(First[IntegerDigits[#]] == 4&)], {n, 100}]  (* Harvey P. Dale, Apr 18 2011 *)

Prog

(PARI) lista(n) = { my(a=[p\10^logint(p, 10)==4 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

Crossrefs

Cf. A000040, A045710, A065680.

Sequence in context: A158799 A157532 A065684 * A065682 A065681 A121242

Adjacent sequences: A065680 A065681 A065682 * A065684 A065685 A065686

Keyword

base,nonn

Author

Reinhard Zumkeller, Nov 13 2001

Status

approved