A045714 Primes with first digit 8.

83, 89, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243

Offset

1,1

Links

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

Mathematica

Flatten[Table[Prime[Range[PrimePi[8 * 10^n] + 1, PrimePi[9 * 10^n]]], {n, 3}]] (* Alonso del Arte, Jul 19 2014 *)

Prog

(Magma) [p: p in PrimesUpTo(10^4) | Intseq(p)[#Intseq(p)] eq 8]; // Bruno Berselli, Jul 19 2014
(Python)
from itertools import chain, count, islice
from sympy import primerange
def A045714_gen(): # generator of terms
    return chain.from_iterable(primerange((m:=10**l)<<3, 9*m) for l in count(0))
A045714_list = list(islice(A045714_gen(), 40)) # Chai Wah Wu, Dec 08 2024
(Python)
from sympy import primepi
def A045714(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(((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))
    return bisection(f, n, n) # Chai Wah Wu, Dec 08 2024

Crossrefs

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.

Column k=8 of A262369.

Sequence in context: A226380 A062677 A284292 * A090156 A220121 A335916

Adjacent sequences: A045711 A045712 A045713 * A045715 A045716 A045717

Keyword

nonn,base,easy

Author

Felice Russo

Extensions

More terms from Erich Friedman.

Status

approved