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%I #12 Jun 15 2018 08:09:44
%S 0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U 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
%N Number of primes <= prime(n) which begin with a 5.
%H Harry J. Smith, <a href="/A065684/b065684.txt">Table of n, a(n) for n = 1..1000</a>
%e a(i) = 1 for 2 < i < 16 and a(16) = 2 as 53 = A000040(16) is the second prime beginning with 5. a(664579) = 72951 (A000040(664579) = 9999991 is the largest prime < 10^7).
%t Accumulate@ Array[Boole[First@ IntegerDigits@ Prime@ # == 5] &, 103] (* _Michael De Vlieger_, Jun 14 2018 *)
%o (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) == 5, a++); p=nextprime(p+1)); write("b065684.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 26 2009
%Y Cf. A065680, A000040.
%K base,nonn
%O 1,16
%A _Reinhard Zumkeller_, Nov 13 2001
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