A065687 Number of primes <= prime(n) which begin with an 8.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Reinhard Zumkeller, Nov 13 2001

Keywords

• base
• nonn

Examples

			83 = A000040(23) is the first prime beginning with an 8, so a(23) = 1 and a(i) = 0 for i < 23. a(664579) = 71038 (A000040(664579) = 9999991 is the largest prime < 10,000,000).
		

Links

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

Crossrefs

Cf. A000040, A045714, A065680.

Programs

Mathematica

Accumulate[If[First[IntegerDigits[#]] == 8, 1, 0]&/@Prime[Range[100]]] (* Vincenzo Librandi, Nov 28 2016 *)

PARI

lista(n) = { my(a=[p\10^logint(p,10)==8 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009