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A038617 Primes not containing the digit '9'.

%I A038617 #57 Jul 23 2025 00:27:24
%S A038617 2,3,5,7,11,13,17,23,31,37,41,43,47,53,61,67,71,73,83,101,103,107,113,
%T A038617 127,131,137,151,157,163,167,173,181,211,223,227,233,241,251,257,263,
%U A038617 271,277,281,283,307,311,313,317,331,337,347,353,367,373,383,401,421
%N A038617 Primes not containing the digit '9'.
%C A038617 Subsequence of primes of A007095. - _Michel Marcus_, Feb 22 2015
%C A038617 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
%H A038617 Indranil Ghosh, <a href="/A038617/b038617.txt">Table of n, a(n) for n = 1..50000</a>
%H A038617 M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a>, OEIS wiki, Jan 12 2020.
%H A038617 James Maynard, <a href="http://arxiv.org/abs/1604.01041">Primes with restricted digits</a>, arXiv:1604.01041 [math.NT], 2016.
%H A038617 James Maynard and Brady Haran, <a href="https://www.youtube.com/watch?v=eeoBCS7IEqs">Primes without a 7</a>, Numberphile video (2019).
%H A038617 <a href="/index/Pri#PrimesWithDigits">Index to entries for primes with digits in a given set</a>
%F A038617 a(n) ~ n^(log 10/log 9) * log(n). - _Charles R Greathouse IV_, Aug 03 2023
%t A038617 Select[Prime[Range[1000]], DigitCount[ # ][[9]] == 0 &] (* _Stefan Steinerberger_, May 20 2006 *)
%o A038617 (Magma) [ p: p in PrimesUpTo(500) | not 9 in Intseq(p) ]; // _Bruno Berselli_, Aug 08 2011
%o A038617 (PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 9), print1(p, ", "));); \\ _Michel Marcus_, Feb 22 2015
%o A038617 (PARI) lista(nn) = forprime (p=2, nn, if (vecmax(digits(p)) != 9, print1(p, ", "))); \\ _Michel Marcus_, Apr 06 2016
%o A038617 (PARI) next_A038617(n)=until((n=nextprime(n+1))==(n=next_A007095(n-1)), ); n \\ _M. F. Hasler_, Jan 14 2020
%o A038617 (Python)
%o A038617 from sympy import isprime
%o A038617 i = 1
%o A038617 while i <= 300:
%o A038617     if "9" not in str(i) and isprime(i):
%o A038617         print(str(i), end=",")
%o A038617     i += 1 # _Indranil Ghosh_, Feb 07 2017
%Y A038617 Intersection of A000040 (primes) and A007095 (numbers with no digit 9).
%Y A038617 Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and this sequence, respectively.
%Y A038617 Primes with other restrictions on digits: A106116, A156756.
%K A038617 nonn,easy,base
%O A038617 1,1
%A A038617 Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998