A065682 - OEIS

%I #16 Dec 15 2024 11:01:30

%S 0,1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,

%T 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,

%U 10,11,12,13,14,15,16,17,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19

%N Number of primes <= prime(n) which begin with a 3.

%H Harry J. Smith, <a href="/A065682/b065682.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 0, a(2) = 1. a(664579) = 75290 (A000040(664579) = 9999991 is the largest prime < 10^7).

%t Accumulate@ Array[Boole[First@ IntegerDigits@ Prime@ # == 3] &, 87] (* _Michael De Vlieger_, Jun 14 2018 *)

%o (PARI) lista(n) = { my(a=[p\10^logint(p,10)==3 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ _Harry J. Smith_, Oct 26 2009

%Y Cf. A000040, A045709, A065680.

%K base,nonn

%O 1,11

%A _Reinhard Zumkeller_, Nov 13 2001