A045711 Primes with first digit 5.

5, 53, 59, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261

Offset

1,1

Comments

Subsequence of A000040.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Mathematica

Select[Table[Prime[n], {n, 5300}], First[IntegerDigits[#]]==5 &] (* Vincenzo Librandi, Aug 08 2014 *)

Prog

(Magma) [p: p in PrimesUpTo(5300) | Intseq(p)[#Intseq(p)] eq 5]; // Vincenzo Librandi, Aug 08 2014
(Python)
from itertools import chain, count, islice
from sympy import primerange
def A045711_gen(): # generator of terms
    return chain.from_iterable(primerange(5*(m:=10**l), 6*m) for l in count(0))
A045711_list = list(islice(A045711_gen(), 40)) # Chai Wah Wu, Dec 08 2024
(Python)
from sympy import primepi
def A045711(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    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))
    return bisection(f, n, n) # Chai Wah Wu, Dec 08 2024

Crossrefs

Column k=5 of A262369.

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.

Sequence in context: A255579 A088712 A257667 * A090153 A188339 A103654

Adjacent sequences: A045708 A045709 A045710 * A045712 A045713 A045714

Keyword

nonn,base,easy

Author

Felice Russo

Extensions

More terms from Erich Friedman.

Leading 5 added by Jaroslav Krizek, Apr 29 2010

Status

approved