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A045715 Primes with first digit 9.

%I A045715 #29 Dec 08 2024 17:19:17
%S A045715 97,907,911,919,929,937,941,947,953,967,971,977,983,991,997,9001,9007,
%T A045715 9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,
%U A045715 9137,9151,9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257
%N A045715 Primes with first digit 9.
%H A045715 Vincenzo Librandi, <a href="/A045715/b045715.txt">Table of n, a(n) for n = 1..1000</a>
%t A045715 Flatten[Table[Prime[Range[PrimePi[9 * 10^n] + 1, PrimePi[10^(n + 1)]]], {n, 3}]] (* _Alonso del Arte_, Jul 19 2014 *)
%o A045715 (Magma) [p: p in PrimesUpTo(10^4) | Intseq(p)[#Intseq(p)] eq 9]; // _Bruno Berselli_, Jul 19 2014
%o A045715 (Magma) [p: p in PrimesInInterval(9*10^n,10^(n+1)), n in [0..3]]; // _Bruno Berselli_, Aug 08 2014
%o A045715 (Python)
%o A045715 from itertools import chain, count, islice
%o A045715 def A045715_gen(): # generator of terms
%o A045715     return chain.from_iterable(primerange(9*(m:=10**l),10*m) for l in count(0))
%o A045715 A045715_list = list(islice(A045715_gen(),40)) # _Chai Wah Wu_, Dec 08 2024
%o A045715 (Python)
%o A045715 from sympy import primepi
%o A045715 def A045715(n):
%o A045715     def bisection(f,kmin=0,kmax=1):
%o A045715         while f(kmax) > kmax: kmax <<= 1
%o A045715         while kmax-kmin > 1:
%o A045715             kmid = kmax+kmin>>1
%o A045715             if f(kmid) <= kmid:
%o A045715                 kmax = kmid
%o A045715             else:
%o A045715                 kmin = kmid
%o A045715         return kmax
%o A045715     def f(x): return n+x+primepi(min(9*(m:=10**(l:=len(str(x))-1))-1,x))-primepi(min(10*m-1,x))+sum(primepi(9*(m:=10**i)-1)-primepi(10*m-1) for i in range(l))
%o A045715     return bisection(f,n,n) # _Chai Wah Wu_, Dec 08 2024
%Y A045715 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 A045715 Column k=9 of A262369.
%K A045715 nonn,base,easy
%O A045715 1,1
%A A045715 _Felice Russo_
%E A045715 More terms from _Erich Friedman_.