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A038611 Primes not containing the digit '3'.

%I A038611 #57 Jul 23 2025 00:25:01
%S A038611 2,5,7,11,17,19,29,41,47,59,61,67,71,79,89,97,101,107,109,127,149,151,
%T A038611 157,167,179,181,191,197,199,211,227,229,241,251,257,269,271,277,281,
%U A038611 401,409,419,421,449,457,461,467,479,487,491,499,509,521,541,547,557
%N A038611 Primes not containing the digit '3'.
%C A038611 Subsequence of primes of A052405. - _Michel Marcus_, Feb 22 2015
%C A038611 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 A038611 Indranil Ghosh, <a href="/A038611/b038611.txt">Table of n, a(n) for n = 1..50000</a>
%H A038611 M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a>, OEIS wiki, Jan 12 2020.
%H A038611 James Maynard, <a href="http://arxiv.org/abs/1604.01041">Primes with restricted digits</a>, arXiv:1604.01041 [math.NT], 2016.
%H A038611 James Maynard and Brady Haran, <a href="https://www.youtube.com/watch?v=eeoBCS7IEqs">Primes without a 7</a>, Numberphile video (2019).
%H A038611 <a href="/index/Pri#PrimesWithDigits">Index to entries for primes with digits in a given set</a>
%F A038611 a(n) ≍ n^(log 10/log 9) log n. - _Charles R Greathouse IV_, Aug 03 2023
%t A038611 Select[Prime[Range[70]], DigitCount[#, 10, 3] == 0 &] (* _Vincenzo Librandi_, Aug 08 2011 *)
%o A038611 (Magma) [ p: p in PrimesUpTo(600) | not 3 in Intseq(p) ]; // _Bruno Berselli_, Aug 08 2011
%o A038611 (PARI)
%o A038611 lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 3), print1(p, ", "));); \\ _Michel Marcus_, Feb 22 2015
%o A038611 (PARI)
%o A038611 ( {A038611_upto(N,M=1)=select( is_A052405, primes([M,N]))} )(350)
%o A038611 (PARI)
%o A038611 next_A038611(n)={until((n=nextprime(n+1))==n=next_A052405(n-1),);n}
%o A038611 ( {A038611_vec(n,M=2)=M--;vector(n,i,M=next_A038611(M))} )(20, 1000)
%o A038611 \\ Get 20 terms >= 1000. See also OEIS wiki page. - _M. F. Hasler_, Jan 14 2020
%o A038611 (Python)
%o A038611 from sympy import isprime
%o A038611 i=j=1
%o A038611 while j<=5000:
%o A038611     if isprime(i) and "3" not in str(i):
%o A038611         print(str(j)+" "+str(i))
%o A038611         j+=1
%o A038611     i+=1 # _Indranil Ghosh_, Feb 07 2017
%Y A038611 Intersection of A000040 (primes) and A052405 (numbers with no digit 3).
%Y A038611 Primes having no digit d = 0..9 are A038618, A038603, A038604, this sequence, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.
%K A038611 nonn,easy,base
%O A038611 1,1
%A A038611 Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
%E A038611 Offset corrected by _Arkadiusz Wesolowski_, Aug 07 2011