A045711 - OEIS

%I #25 Dec 08 2024 17:18:35

%S 5,53,59,503,509,521,523,541,547,557,563,569,571,577,587,593,599,5003,

%T 5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,

%U 5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261

%N Primes with first digit 5.

%C Subsequence of A000040.

%H Vincenzo Librandi, <a href="/A045711/b045711.txt">Table of n, a(n) for n = 1..5000</a>

%t Select[Table[Prime[n], {n, 5300}], First[IntegerDigits[#]]==5 &] (* _Vincenzo Librandi_, Aug 08 2014 *)

%o (Magma) [p: p in PrimesUpTo(5300) | Intseq(p)[#Intseq(p)] eq 5]; // _Vincenzo Librandi_, Aug 08 2014

%o (Python)

%o from itertools import chain, count, islice

%o from sympy import primerange

%o def A045711_gen(): # generator of terms

%o     return chain.from_iterable(primerange(5*(m:=10**l),6*m) for l in count(0))

%o A045711_list = list(islice(A045711_gen(),40)) # _Chai Wah Wu_, Dec 08 2024

%o (Python)

%o from sympy import primepi

%o def A045711(n):

%o     def bisection(f,kmin=0,kmax=1):

%o         while f(kmax) > kmax: kmax <<= 1

%o         while kmax-kmin > 1:

%o             kmid = kmax+kmin>>1

%o             if f(kmid) <= kmid:

%o                 kmax = kmid

%o             else:

%o                 kmin = kmid

%o         return kmax

%o     def f(x): return n+x+primepi(min(5*(m:=10**(l:=len(str(x))-1))-1,x))-primepi(min(6*m-1,x))+sum(primepi(5*(m:=10**i)-1)-primepi(6*m-1) for i in range(l))

%o     return bisection(f,n,n) # _Chai Wah Wu_, Dec 08 2024

%Y Column k=5 of A262369.

%Y 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.

%K nonn,base,easy

%O 1,1

%A _Felice Russo_

%E More terms from _Erich Friedman_.

%E Leading 5 added by _Jaroslav Krizek_, Apr 29 2010