A038614 - OEIS

%I #49 Aug 04 2023 18:59:31

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,71,73,79,83,89,97,101,

%T 103,107,109,113,127,131,137,139,149,151,157,173,179,181,191,193,197,

%U 199,211,223,227,229,233,239,241,251,257,271,277,281,283,293,307,311

%N Primes not containing the digit '6'.

%C Subsequence of primes of A052414. - _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 Robert Israel, <a href="/A038614/b038614.txt">Table of n, a(n) for n = 1..10000</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 Intersection of A000040 and A052414. - _M. F. Hasler_, Jan 12 2020

%F a(n) ~ n^(log 10/log 9) log n. - _Charles R Greathouse IV_, Aug 03 2023

%p no6:= proc(n) option remember;

%p   n mod 10 <> 6 and procname(floor(n/10))

%p end proc:

%p no6(0):= true:

%p select(no6 and isprime, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Mar 16 2017

%t Select[Prime[Range[70]], DigitCount[#, 10, 6] == 0 &] (* _Vincenzo Librandi_, Aug 08 2011 *)

%o (Magma) [ p: p in PrimesUpTo(400) | not 6 in Intseq(p) ]; // _Bruno Berselli_, Aug 08 2011

%o (PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 6), print1(p, ", "));); \\ _Michel Marcus_, Feb 22 2015

%o (PARI)

%o select( {is_A038614(n)=is_A052414(n)&&isprime(n)}, [1..350]) \\ see A052414

%o (A038614_upto(n)=select( is_A038614, primes([1,n])))(350) \\ needs the above

%o next_A038614(n)={until(isprime(n), n=next_A052414(nextprime(n+1)-1));n}

%o (A038614_vec(n)=vector(n,i,n=next_A038614(if(i>1,n))))(66) \\ _M. F. Hasler_, Jan 12 2020

%Y Intersection of A000040 (primes) and A052414 (numbers with no digit 6).

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