A045715 Primes with first digit 9.

97, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

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

Prog

(Magma) [p: p in PrimesUpTo(10^4) | Intseq(p)[#Intseq(p)] eq 9]; // Bruno Berselli, Jul 19 2014
(Magma) [p: p in PrimesInInterval(9*10^n, 10^(n+1)), n in [0..3]]; // Bruno Berselli, Aug 08 2014
(Python)
from itertools import chain, count, islice
def A045715_gen(): # generator of terms
    return chain.from_iterable(primerange(9*(m:=10**l), 10*m) for l in count(0))
A045715_list = list(islice(A045715_gen(), 40)) # Chai Wah Wu, Dec 08 2024
(Python)
from sympy import primepi
def A045715(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(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))
    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=9 of A262369.

Sequence in context: A216380 A133535 A321051 * A113891 A090157 A162674

Adjacent sequences: A045712 A045713 A045714 * A045716 A045717 A045718

Keyword

nonn,base,easy

Author

Felice Russo

Extensions

More terms from Erich Friedman.

Status

approved