A038603 - OEIS

%I #63 Aug 04 2023 18:59:16

%S 2,3,5,7,23,29,37,43,47,53,59,67,73,79,83,89,97,223,227,229,233,239,

%T 257,263,269,277,283,293,307,337,347,349,353,359,367,373,379,383,389,

%U 397,409,433,439,443,449,457,463,467,479,487,499,503,509,523,547,557

%N Primes not containing the digit '1'.

%C Subsequence of A132080. - _Reinhard Zumkeller_, Aug 09 2007

%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="/A038603/b038603.txt">Table of n, a(n) for n = 1..50000</a> (terms 1..1000 from R. Zumkeller)

%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, 1] == 0 &] (* _Vincenzo Librandi_, Aug 09 2011 *)

%o (Magma) [ p: p in PrimesUpTo(600) | not 1 in Intseq(p) ];  // _Bruno Berselli_, Aug 08 2011

%o (PARI) is(n)=if(isprime(n),n=vecsort(eval(Vec(Str(n))),,8);n[1]>1||(!n[1]&&n[2]>1)) \\ _Charles R Greathouse IV_, Aug 09 2011

%o (PARI) is(n)=!vecsearch(vecsort(digits(n)),1) && isprime(n) \\ _Charles R Greathouse IV_, Oct 03 2012

%o (PARI) next_A038603(n)=until((n=nextprime(n+1))==n=next_A052383(n-1),);n \\ Compute least a(k) > n. See A052383. - _M. F. Hasler_, Jan 14 2020

%o (Python)

%o from sympy import nextprime

%o i=p=1

%o while i<=500:

%o     p = nextprime(p)

%o     if '1' not in str(p):

%o         print(str(i)+" "+str(p))

%o         i+=1

%o # _Indranil Ghosh_, Feb 07 2017, edited by _M. F. Hasler_, Jan 15 2020

%o # See the OEIS Wiki page for more efficient programs. - _M. F. Hasler_, Jan 14 2020

%Y Intersection of A000040 (primes) and A052383 (numbers with no digit 1).

%Y Primes having no digit d = 0..9 are A038618, this sequence, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

%Y Primes with other restrictions on digits: A106116, A156756.

%K nonn,easy,base

%O 1,1

%A Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998