OFFSET
1,1
COMMENTS
Subsequence of primes of A007095. - Michel Marcus, Feb 22 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..50000
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
FORMULA
a(n) ~ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023
MATHEMATICA
Select[Prime[Range[1000]], DigitCount[ # ][[9]] == 0 &] (* Stefan Steinerberger, May 20 2006 *)
PROG
(Magma) [ p: p in PrimesUpTo(500) | not 9 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 9), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI) lista(nn) = forprime (p=2, nn, if (vecmax(digits(p)) != 9, print1(p, ", "))); \\ Michel Marcus, Apr 06 2016
(PARI) next_A038617(n)=until((n=nextprime(n+1))==(n=next_A007095(n-1)), ); n \\ M. F. Hasler, Jan 14 2020
(Python)
from sympy import isprime
i = 1
while i <= 300:
if "9" not in str(i) and isprime(i):
print(str(i), end=", ")
i += 1 # Indranil Ghosh, Feb 07 2017
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
STATUS
approved