A038611 -id:A038611 - cp's OEIS frontend

A038618 Primes not containing the digit '0'.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293

Offset: 1

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

Complement of A056709 with respect to primes (A000040). - Lekraj Beedassy, Jul 04 2010

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
René-Louis Clerc, Nombres premiers primaires et nombres premiers secondaires , 2025.
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Eric Weisstein's World of Mathematics, Zerofree.
Index to entries for primes with digits in a given set

Cf. A010051, A168046, A384793, A384794.
Subsequence of A000040 (primes), A052382 (zeroless numbers) and A195943.
Primes having no digit d = 0..9 are this sequence, A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

a038618 n = a038618_list !! (n-1)
a038618_list = filter ((== 1) . a168046) a000040_list
-- Reinhard Zumkeller, Apr 07 2014, Sep 27 2011

[ p: p in PrimesUpTo(300) | not 0 in Intseq(p) ];  // Bruno Berselli, Aug 08 2011

Select[Prime[Range[70]], DigitCount[#, 10, 0] == 0 &] (* Vincenzo Librandi, Aug 09 2011 *)

is(n)=if(isprime(n),n=vecsort(eval(Vec(Str(n))),,8);n[1]>0) \\ Charles R Greathouse IV, Aug 09 2011

lista(nn) = forprime (p=2, nn, if (vecmin(digits(p)), print1(p, ", "))); \\ Michel Marcus, Apr 06 2016

next_A038618(n)=until(vecmin(digits(n=nextprime(next_A052382(n)))),);n \\ Cf. OEIS Wiki page (LINKS) for other programs. - M. F. Hasler, Jan 12 2020

from sympy import primerange
def aupto(N): return [p for p in primerange(1, N+1) if '0' not in str(p)]
print(aupto(300)) # Michael S. Branicky, Mar 11 2022

Intersection of A052382 (zeroless numbers) and A000040 (primes); A168046(a(n))*A010051(a(n)) = 1. - Reinhard Zumkeller, Dec 01 2009

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

A038603 Primes not containing the digit '1'.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 223, 227, 229, 233, 239, 257, 263, 269, 277, 283, 293, 307, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 409, 433, 439, 443, 449, 457, 463, 467, 479, 487, 499, 503, 509, 523, 547, 557

Offset: 1

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

Subsequence of A132080. - Reinhard Zumkeller, Aug 09 2007

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

Indranil Ghosh, Table of n, a(n) for n = 1..50000 (terms 1..1000 from R. Zumkeller)
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

Intersection of A000040 (primes) and A052383 (numbers with no digit 1).
Primes having no digit d = 0..9 are A038618, this sequence, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.
Primes with other restrictions on digits: A106116, A156756.

[ p: p in PrimesUpTo(600) | not 1 in Intseq(p) ];  // Bruno Berselli, Aug 08 2011

Select[Prime[Range[70]], DigitCount[#, 10, 1] == 0 &] (* Vincenzo Librandi, Aug 09 2011 *)

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

is(n)=!vecsearch(vecsort(digits(n)),1) && isprime(n) \\ Charles R Greathouse IV, Oct 03 2012

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

from sympy import nextprime
i=p=1
while i<=500:
    p = nextprime(p)
    if '1' not in str(p):
        print(str(i)+" "+str(p))
        i+=1
# Indranil Ghosh, Feb 07 2017, edited by M. F. Hasler, Jan 15 2020
# See the OEIS Wiki page for more efficient programs. - M. F. Hasler, Jan 14 2020

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

A038615 Primes not containing the digit '7'.

Original entry on oeis.org

2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 59, 61, 83, 89, 101, 103, 109, 113, 131, 139, 149, 151, 163, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 251, 263, 269, 281, 283, 293, 311, 313, 331, 349, 353, 359, 383, 389, 401, 409, 419, 421, 431, 433, 439

Offset: 1

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

Subsequence of primes of A052419. - Michel Marcus, Feb 22 2015

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

Alois P. Heinz, Table of n, a(n) for n = 1..20000
Marianne Freiberger, Primes without 7s, +plus magazine, August 2016.
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

Cf. A000040, A052419.

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, this sequence, A038616, and A038617, respectively.

[ p: p in PrimesUpTo(500) | not 7 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Select[Prime[Range[70]], DigitCount[#, 10, 7] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 7), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

(A038615_upto(N)=select( is_A052419, primes([1,N])))(444) \\ i.e.: {is_A038615(n)=is_A052419(n)&&isprime(n)}; {is_A052419(n)=!setsearch(Set(digits(n)),7)}. - M. F. Hasler, Jan 11 2020

Intersection of A000040 (primes) and A052419 (numbers with no digit 7). - M. F. Hasler, Jan 11 2020

a(n) ~ n^(log 10/log 9) * log(n). - Charles R Greathouse IV, Aug 03 2023

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038617 Primes not containing the digit '9'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 83, 101, 103, 107, 113, 127, 131, 137, 151, 157, 163, 167, 173, 181, 211, 223, 227, 233, 241, 251, 257, 263, 271, 277, 281, 283, 307, 311, 313, 317, 331, 337, 347, 353, 367, 373, 383, 401, 421

Offset: 1

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

Subsequence of primes of A007095. - Michel Marcus, Feb 22 2015

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

Indranil Ghosh, Table of n, a(n) for n = 1..50000
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

Intersection of A000040 (primes) and A007095 (numbers with no digit 9).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and this sequence, respectively.
Primes with other restrictions on digits: A106116, A156756.

[ p: p in PrimesUpTo(500) | not 9 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Select[Prime[Range[1000]], DigitCount[ # ][[9]] == 0 &] (* Stefan Steinerberger, May 20 2006 *)

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 9), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

lista(nn) = forprime (p=2, nn, if (vecmax(digits(p)) != 9, print1(p, ", "))); \\ Michel Marcus, Apr 06 2016

next_A038617(n)=until((n=nextprime(n+1))==(n=next_A007095(n-1)), ); n \\ M. F. Hasler, Jan 14 2020

from sympy import isprime
i = 1
while i <= 300:
    if "9" not in str(i) and isprime(i):
        print(str(i), end=",")
    i += 1 # Indranil Ghosh, Feb 07 2017

a(n) ~ n^(log 10/log 9) * log(n). - Charles R Greathouse IV, Aug 03 2023

A038604 Primes not containing the digit '2'.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397

Offset: 1

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

Subsequence of primes of A052404. - Michel Marcus, Feb 21 2015

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

Indranil Ghosh, Table of n, a(n) for n = 1..50000
M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

Cf. A000040, A052404.
Subsequence of A065091 (odd primes).
Primes having no digit d = 0..9 are A038618, A038603, this sequence, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

[ p: p in PrimesUpTo(400) | not 2 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Select[Prime[Range[70]], DigitCount[#, 10, 2] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

lista(nn, d=2) = {forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), d), print1(p, ", ")););} \\ Michel Marcus, Feb 21 2015

select( {is_A038604(n)=is_A052404(n)&&isprime(n)}, [1..400]) \\ see Wiki for more
{next_A038604(n)=until((n==nextprime(n+1))==n=next_A052404(n-1),);n} \\ M. F. Hasler, Jan 12 2020

from sympy import isprime, nextprime
def is_A038604(n): return str(n).find('2')<0 and isprime(n)
def next_A038604(n): # get smallest term > n
    while True:
        n = nextprime(n); s = str(n); t = s.find('2')
        if t < 0: return n
        t = 10**(len(s)-1-t); n += t - n%t
def A038604_upto(stop=math.inf, start=3):
    while start < stop: yield start; start = next_A038604(start)
list(A038604_upto(400))
# M. F. Hasler, Jan 12 2020

Intersection of A000040 and A052404. - M. F. Hasler, Jan 11 2020

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038612 Primes not containing the digit '4'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 293

Offset: 1

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

Subsequence of primes of A052406. - Michel Marcus, Feb 22 2015

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

Jason Bard, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

Intersection of A000040 (primes) and A052406 (numbers without digit 4).

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, this sequence, A038613, A038614, A038615, A038616, and A038617, respectively.

[ p: p in PrimesUpTo(300) | not 4 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Select[Prime[Range[70]], DigitCount[#, 10, 4] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 4), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

( {A038612_upto(N)=select( is_A052406, primes([1, N]))} )(444) \\ or better:
next_A038612(n)={until(isprime(n), n=next_A052406(nextprime(n+1)-1)); n}
( {A038612_vec(n,M=1)=M--;vector(n,i, n=next_A038612(if(i>1, n)))} )(20, 1000)
\\ (See the OEIS wiki page for more.) - M. F. Hasler, Jan 12 2020

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038614 Primes not containing the digit '6'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 271, 277, 281, 283, 293, 307, 311

Offset: 1

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

Subsequence of primes of A052414. - Michel Marcus, Feb 22 2015

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

Robert Israel, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

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

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, this sequence, A038615, A038616, and A038617, respectively.

[ p: p in PrimesUpTo(400) | not 6 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

no6:= proc(n) option remember;
  n mod 10 <> 6 and procname(floor(n/10))
end proc:
no6(0):= true:
select(no6 and isprime, [2,seq(i,i=3..1000,2)]); # Robert Israel, Mar 16 2017

Select[Prime[Range[70]], DigitCount[#, 10, 6] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 6), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

select( {is_A038614(n)=is_A052414(n)&&isprime(n)}, [1..350]) \\ see A052414
(A038614_upto(n)=select( is_A038614, primes([1,n])))(350) \\ needs the above
next_A038614(n)={until(isprime(n), n=next_A052414(nextprime(n+1)-1));n}
(A038614_vec(n)=vector(n,i,n=next_A038614(if(i>1,n))))(66) \\ M. F. Hasler, Jan 12 2020

Intersection of A000040 and A052414. - M. F. Hasler, Jan 12 2020

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038613 Primes not containing the digit '5'.

Original entry on oeis.org

2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset: 1

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

Subsequence of primes of A052413. - Michel Marcus, Feb 22 2015

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

			From _M. F. Hasler_, Jan 14 2020: (Start)
After a(85) = 499, the next prime without digit 5 is a(86) = 601.
After a(3734) = 49999, the next term is a(3735) = 60013.
After a(27273) = 499979, the next term is 600011.
After a(206276) = 4999999, the next term is 6000011. (End)

Jason Bard, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

Intersection of A000040 (primes) and A052413 (numbers with no digit 5).

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, this sequence, A038614, A038615, A038616, and A038617, respectively.

[ p: p in PrimesUpTo(400) | not 5 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Select[Prime[Range[70]], DigitCount[#, 10, 5] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 5), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

(A038613_upto(n)=select( is_A052413, primes([1, n])))(350) \\ see A052413
next_A038613(n)={until(isprime(n), n=next_A052413(nextprime(n+1)-1)); n}
( {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

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038616 Primes not containing the digit '8'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 293, 307

Offset: 1

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

Subsequence of primes of A052421. - Michel Marcus, Feb 22 2015

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

Indranil Ghosh, Table of n, a(n) for n = 1..50000
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

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

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, this sequence, and A038617, respectively.

[ p: p in PrimesUpTo(400) | not 8 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Select[Prime[Range[70]], DigitCount[#, 10, 8] == 0 &] (* Harvey P. Dale, Jan 24 2011 *)

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 8), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

next_A038616(n)=until((n=nextprime(n+1))==(n=next_A052421(n-1)), ); n \\ M. F. Hasler, Jan 14 2020

a(n) ~ n^(log 10/log 9) * log(n). - Charles R Greathouse IV, Aug 03 2023

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A052405 Numbers without 3 as a digit.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

This sequence also represents the minimal number of straight lines of a covering tree to cover n X n points arranged in a symmetrical grid. - Marco Ripà, Sep 20 2018

			22 has no 3s among its digits, hence it is in the sequence.
23 has one 3 among its digits, hence it is not in the sequence.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
Index entries for 10-automatic sequences.

Cf. A004178, A004722, A038611 (subset of primes), A082832 (Kempner series).
Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).
Cf. A011533 (complement).

a052405 = f . subtract 1 where
   f 0 = 0
   f v = 10 * f w + if r > 2 then r + 1 else r  where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 3 in Intseq(n) ];  // Bruno Berselli, May 28 2011

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<3, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

Select[Range[0, 89], DigitCount[#, 10, 3] == 0 &] (* Alonso del Arte, Oct 16 2012 *)

is(n)=n=digits(n);for(i=1,#n,if(n[i]==3,return(0)));1 \\ Charles R Greathouse IV, Oct 16 2012
apply( {A052405(n)=fromdigits(apply(d->d+(d>2),digits(n-1,9)))}, [1..99]) \\ a(n)
next_A052405(n, d=digits(n+=1))={for(i=1, #d, d[i]==3&& return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used in A038611. \\ M. F. Hasler, Jan 11 2020

from gmpy2 import digits
def A052405(n): return int(digits(n-1,9).translate(str.maketrans('345678','456789'))) # Chai Wah Wu, Jun 28 2025

seq 0 1000 | grep -v 3; # Joerg Arndt, May 29 2011

a(n) >> n^k with k = log(10)/log(9) = 1.0479.... - Charles R Greathouse IV, Oct 16 2012
a(n) = replace digits d > 2 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
Sum_{n>1} 1/a(n) = A082832 = 20.569877... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 14 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

cp's OEIS Frontend

A038618 Primes not containing the digit '0'.

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A038603 Primes not containing the digit '1'.

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A038615 Primes not containing the digit '7'.

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A038617 Primes not containing the digit '9'.

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A038604 Primes not containing the digit '2'.

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A038612 Primes not containing the digit '4'.

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