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A045713
Primes with first digit 7.
22
7, 71, 73, 79, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283
OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..5000
MATHEMATICA
Select[ Table[ Prime[ n ], {n, 1000} ], First[ IntegerDigits[ # ]]==7& ]
PROG
(Magma) [p: p in PrimesUpTo(7300) | Intseq(p)[#Intseq(p)] eq 7]; // Vincenzo Librandi, Aug 08 2014
(Python)
from itertools import chain, count, islice
from sympy import primerange
def A045713_gen(): # generator of terms
return chain.from_iterable(primerange(7*(m:=10**l), m<<3) for l in count(0))
(Python)
from sympy import primepi
def A045713(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(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))
return bisection(f, n, n) # Chai Wah Wu, Dec 08 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
More terms from Erich Friedman.
Corrected by Jud McCranie, Jan 03 2001
a(13)=757 added from Vincenzo Librandi, Aug 08 2014
STATUS
approved