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%I #43 Aug 04 2023 18:59:01
%S 2,3,7,11,13,17,19,23,29,31,37,41,43,47,61,67,71,73,79,83,89,97,101,
%T 103,107,109,113,127,131,137,139,149,163,167,173,179,181,191,193,197,
%U 199,211,223,227,229,233,239,241,263,269,271,277,281,283,293,307,311
%N Primes not containing the digit '5'.
%C Subsequence of primes of A052413. - _Michel Marcus_, Feb 22 2015
%C 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 M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a>, OEIS wiki, Jan 12 2020.
%H James Maynard, <a href="http://arxiv.org/abs/1604.01041">Primes with restricted digits</a>, arXiv:1604.01041 [math.NT], 2016.
%H James Maynard and Brady Haran, <a href="https://www.youtube.com/watch?v=eeoBCS7IEqs">Primes without a 7</a>, Numberphile video (2019).
%F a(n) ~ n^(log 10/log 9) log n. - _Charles R Greathouse IV_, Aug 03 2023
%e From _M. F. Hasler_, Jan 14 2020: (Start)
%e After a(85) = 499, the next prime without digit 5 is a(86) = 601.
%e After a(3734) = 49999, the next term is a(3735) = 60013.
%e After a(27273) = 499979, the next term is 600011.
%e After a(206276) = 4999999, the next term is 6000011. (End)
%t Select[Prime[Range[70]], DigitCount[#, 10, 5] == 0 &] (* _Vincenzo Librandi_, Aug 08 2011 *)
%o (Magma) [ p: p in PrimesUpTo(400) | not 5 in Intseq(p) ]; // _Bruno Berselli_, Aug 08 2011
%o (PARI)
%o lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 5), print1(p, ", "));); \\ _Michel Marcus_, Feb 22 2015
%o (A038613_upto(n)=select( is_A052413, primes([1, n])))(350) \\ see A052413
%o next_A038613(n)={until(isprime(n), n=next_A052413(nextprime(n+1)-1)); n}
%o ( {A038613_vec(n, M=1)=M--;vector(n, i, M=next_A038613(M))} )(20, 1000) \\ Compute n terms >= M. See also the OEIS wiki page. - _M. F. Hasler_, Jan 14 2020
%Y Intersection of A000040 (primes) and A052413 (numbers with no digit 5).
%Y Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, this sequence, A038614, A038615, A038616, and A038617, respectively.
%K nonn,easy,base
%O 1,1
%A Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
%E Offset corrected by _Arkadiusz Wesolowski_, Aug 07 2011
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