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Primes not containing digit '8'.
12

%I #48 Aug 04 2023 18:59:08

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,97,101,

%T 103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,191,193,

%U 197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,293,307

%N Primes not containing digit '8'.

%C Subsequence of primes of A052421. - _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 Indranil Ghosh, <a href="/A038616/b038616.txt">Table of n, a(n) for n = 1..50000</a>

%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

%t Select[Prime[Range[70]], DigitCount[#, 10, 8] == 0 &] (* _Harvey P. Dale_, Jan 24 2011 *)

%o (Magma) [ p: p in PrimesUpTo(400) | not 8 in Intseq(p) ]; // _Bruno Berselli_, Aug 08 2011

%o (PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 8), print1(p, ", "));); \\ _Michel Marcus_, Feb 22 2015

%o (PARI) next_A038616(n)=until((n=nextprime(n+1))==(n=next_A052421(n-1)), ); n \\ _M. F. Hasler_, Jan 14 2020

%Y Intersection of A000040 (primes) and A052421 (numbers with no 8).

%Y Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, this sequence, 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