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A045713 Primes with first digit 7.

%I A045713 #32 Dec 08 2024 17:19:01
%S A045713 7,71,73,79,701,709,719,727,733,739,743,751,757,761,769,773,787,797,
%T A045713 7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,
%U A045713 7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283
%N A045713 Primes with first digit 7.
%H A045713 Vincenzo Librandi, <a href="/A045713/b045713.txt">Table of n, a(n) for n = 1..5000</a>
%t A045713 Select[ Table[ Prime[ n ], {n, 1000} ], First[ IntegerDigits[ # ]]==7& ]
%o A045713 (Magma) [p: p in PrimesUpTo(7300) | Intseq(p)[#Intseq(p)] eq 7]; // _Vincenzo Librandi_, Aug 08 2014
%o A045713 (Python)
%o A045713 from itertools import chain, count, islice
%o A045713 from sympy import primerange
%o A045713 def A045713_gen(): # generator of terms
%o A045713     return chain.from_iterable(primerange(7*(m:=10**l),m<<3) for l in count(0))
%o A045713 A045713_list = list(islice(A045713_gen(),40)) # _Chai Wah Wu_, Dec 08 2024
%o A045713 (Python)
%o A045713 from sympy import primepi
%o A045713 def A045713(n):
%o A045713     def bisection(f,kmin=0,kmax=1):
%o A045713         while f(kmax) > kmax: kmax <<= 1
%o A045713         while kmax-kmin > 1:
%o A045713             kmid = kmax+kmin>>1
%o A045713             if f(kmid) <= kmid:
%o A045713                 kmax = kmid
%o A045713             else:
%o A045713                 kmin = kmid
%o A045713         return kmax
%o A045713     def f(x): return n+x+primepi(min(7*(m:=10**(l:=len(str(x))-1))-1,x))-primepi(min((m<<3)-1,x))+sum(primepi(7*(m:=10**i)-1)-primepi((m<<3)-1) for i in range(l))
%o A045713     return bisection(f,n,n) # _Chai Wah Wu_, Dec 08 2024
%Y A045713 Cf. A000040.
%Y A045713 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 A045713 Column k=7 of A262369.
%K A045713 nonn,base
%O A045713 1,1
%A A045713 _Felice Russo_
%E A045713 More terms from _Erich Friedman_.
%E A045713 Corrected by _Jud McCranie_, Jan 03 2001
%E A045713 a(13)=757 added from _Vincenzo Librandi_, Aug 08 2014