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A045714 Primes with first digit 8.

%I A045714 #32 Dec 08 2024 17:19:10
%S A045714 83,89,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,
%T A045714 8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,
%U A045714 8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243
%N A045714 Primes with first digit 8.
%H A045714 Vincenzo Librandi, <a href="/A045714/b045714.txt">Table of n, a(n) for n = 1..5000</a>
%t A045714 Flatten[Table[Prime[Range[PrimePi[8 * 10^n] + 1, PrimePi[9 * 10^n]]], {n, 3}]] (* _Alonso del Arte_, Jul 19 2014 *)
%o A045714 (Magma) [p: p in PrimesUpTo(10^4) | Intseq(p)[#Intseq(p)] eq 8]; // _Bruno Berselli_, Jul 19 2014
%o A045714 (Python)
%o A045714 from itertools import chain, count, islice
%o A045714 from sympy import primerange
%o A045714 def A045714_gen(): # generator of terms
%o A045714     return chain.from_iterable(primerange((m:=10**l)<<3,9*m) for l in count(0))
%o A045714 A045714_list = list(islice(A045714_gen(),40)) # _Chai Wah Wu_, Dec 08 2024
%o A045714 (Python)
%o A045714 from sympy import primepi
%o A045714 def A045714(n):
%o A045714     def bisection(f,kmin=0,kmax=1):
%o A045714         while f(kmax) > kmax: kmax <<= 1
%o A045714         while kmax-kmin > 1:
%o A045714             kmid = kmax+kmin>>1
%o A045714             if f(kmid) <= kmid:
%o A045714                 kmax = kmid
%o A045714             else:
%o A045714                 kmin = kmid
%o A045714         return kmax
%o A045714     def f(x): return n+x+primepi(min(((m:=10**(l:=len(str(x))-1))<<3)-1,x))-primepi(min(9*m-1,x))+sum(primepi(((m:=10**i)<<3)-1)-primepi(9*m-1) for i in range(l))
%o A045714     return bisection(f,n,n) # _Chai Wah Wu_, Dec 08 2024
%Y A045714 For primes with initial digit d (1 <= d <= 9) see A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715; A073517, A073516, A073515, A073514, A073513, A073512, A073511, A073510, A073509.
%Y A045714 Column k=8 of A262369.
%K A045714 nonn,base,easy
%O A045714 1,1
%A A045714 _Felice Russo_
%E A045714 More terms from _Erich Friedman_.