OFFSET
1,1
COMMENTS
Subsequence of primes of A052404. - Michel Marcus, Feb 21 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[70]], DigitCount[#, 10, 2] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
PROG
(Magma) [ p: p in PrimesUpTo(400) | not 2 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) lista(nn, d=2) = {forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), d), print1(p, ", ")); ); } \\ Michel Marcus, Feb 21 2015
(PARI)
(Python)
from sympy import isprime, nextprime
def is_A038604(n): return str(n).find('2')<0 and isprime(n)
def next_A038604(n): # get smallest term > n
while True:
n = nextprime(n); s = str(n); t = s.find('2')
if t < 0: return n
t = 10**(len(s)-1-t); n += t - n%t
def A038604_upto(stop=math.inf, start=3):
while start < stop: yield start; start = next_A038604(start)
list(A038604_upto(400))
# M. F. Hasler, Jan 12 2020
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Aug 07 2011
STATUS
approved