cp's OEIS Frontend

A038613 Primes not containing the digit '5'.

%I A038613 #54 Jul 23 2025 00:25:30
%S A038613 2,3,7,11,13,17,19,23,29,31,37,41,43,47,61,67,71,73,79,83,89,97,101,
%T A038613 103,107,109,113,127,131,137,139,149,163,167,173,179,181,191,193,197,
%U A038613 199,211,223,227,229,233,239,241,263,269,271,277,281,283,293,307,311
%N A038613 Primes not containing the digit '5'.
%C A038613 Subsequence of primes of A052413. - _Michel Marcus_, Feb 22 2015
%C A038613 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 A038613 Jason Bard, <a href="/A038613/b038613.txt">Table of n, a(n) for n = 1..10000</a>
%H A038613 M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a>, OEIS wiki, Jan 12 2020.
%H A038613 James Maynard, <a href="http://arxiv.org/abs/1604.01041">Primes with restricted digits</a>, arXiv:1604.01041 [math.NT], 2016.
%H A038613 James Maynard and Brady Haran, <a href="https://www.youtube.com/watch?v=eeoBCS7IEqs">Primes without a 7</a>, Numberphile video (2019).
%H A038613 <a href="/index/Pri#PrimesWithDigits">Index to entries for primes with digits in a given set</a>
%F A038613 a(n) ≍ n^(log 10/log 9) log n. - _Charles R Greathouse IV_, Aug 03 2023
%e A038613 From _M. F. Hasler_, Jan 14 2020: (Start)
%e A038613 After a(85) = 499, the next prime without digit 5 is a(86) = 601.
%e A038613 After a(3734) = 49999, the next term is a(3735) = 60013.
%e A038613 After a(27273) = 499979, the next term is 600011.
%e A038613 After a(206276) = 4999999, the next term is 6000011. (End)
%t A038613 Select[Prime[Range[70]], DigitCount[#, 10, 5] == 0 &] (* _Vincenzo Librandi_, Aug 08 2011 *)
%o A038613 (Magma) [ p: p in PrimesUpTo(400) | not 5 in Intseq(p) ]; // _Bruno Berselli_, Aug 08 2011
%o A038613 (PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 5), print1(p, ", "));); \\ _Michel Marcus_, Feb 22 2015
%o A038613 (PARI) (A038613_upto(n)=select( is_A052413, primes([1, n])))(350) \\ see A052413
%o A038613 next_A038613(n)={until(isprime(n), n=next_A052413(nextprime(n+1)-1)); n}
%o A038613 ( {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 A038613 Intersection of A000040 (primes) and A052413 (numbers with no digit 5).
%Y A038613 Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, this sequence, A038614, A038615, A038616, and A038617, respectively.
%K A038613 nonn,easy,base
%O A038613 1,1
%A A038613 Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
%E A038613 Offset corrected by _Arkadiusz Wesolowski_, Aug 07 2011