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

1,24

Links

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

Example

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).

Mathematica

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

Prog

(PARI) digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) } MSD(x)= { return(x\10^(digitsIn(x)-1)) } { a=0; p=2; for (n=1, 1000, q=prime(n); while (p <= q, if(MSD(p) == 8, a++); p=nextprime(p+1)); write("b065687.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 26 2009

Crossrefs

Cf. A000040, A065680.

Sequence in context: A280560 A044932 A211669 * A300403 A077433 A065685

Adjacent sequences: A065684 A065685 A065686 * A065688 A065689 A065690

Keyword

base,nonn

Author

Reinhard Zumkeller, Nov 13 2001

Status

approved