A020472 -id:A020472 - cp's OEIS frontend

A199325 Primes having only {0, 1, 5} as digits.

5, 11, 101, 151, 1051, 1151, 1511, 5011, 5051, 5101, 5501, 10111, 10151, 10501, 11551, 15101, 15511, 15551, 50051, 50101, 50111, 50551, 51001, 51151, 51511, 51551, 55001, 55051, 55501, 55511, 100151, 100501, 100511, 101051, 101111, 101501, 110051, 110501, 115001, 115151, 150001, 150011, 150151, 150551

Offset: 1

M. F. Hasler, Nov 05 2011

Robert Israel, Table of n, a(n) for n = 1..10000
Index to entries about primes with digits in a given set

Cf. A020449 - A020472, A199326 - A199329, A061247, A199340 - A199349.

[p: p in PrimesUpTo(160000) | Set(Intseq(p)) subset [0, 1, 5]]; // Vincenzo Librandi, Apr 22 2014

N:= 10000: # to get the first N terms
count:= 0:
allowed:= {0,1,5}:
nallowed:= nops(allowed):
subst:= seq(i=allowed[i+1],i=0..nallowed-1):
for d from 0 while count < N do
  for x1 from 1 to nallowed-1 while count < N do
    for t from 0 to nallowed^d-1 while count < N do
      L:= subs(subst,convert(x1*nallowed^d+t,base,nallowed));
      X:= add(L[i]*10^(i-1),i=1..d+1);
      if isprime(X) then
          count:= count+1;
          A[count]:= X;
      fi
od od od:
seq(A[n],n=1..N); # Robert Israel, Apr 20 2014

Select[FromDigits/@Tuples[{0,1,5},6],PrimeQ] (* Harvey P. Dale, Jul 23 2021 *)

L=[0,1,5];for(d=1,6,u=vector(d,i,10^(d-i))~;forvec(v=vector(d,i,[1+(i==1 & !L[1]),#L]),ispseudoprime(t=vector(d,i,L[v[i]])*u)&print1(t",")))  /* see A199327 for a function a(n) */

A199329 Primes having only {0, 1, 9} as digits.

Original entry on oeis.org

11, 19, 101, 109, 191, 199, 911, 919, 991, 1009, 1019, 1091, 1109, 1901, 1999, 9001, 9011, 9091, 9109, 9199, 9901, 10009, 10091, 10099, 10111, 10909, 11119, 11909, 19001, 19009, 19919, 19991, 90001, 90011, 90019, 90191, 90199, 90901, 90911, 91009, 91019, 91099, 91199, 91909, 99109, 99119, 99191, 99901, 99991

Offset: 1

M. F. Hasler, Nov 05 2011

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries about primes with digits in a given set

Cf. A020449 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199327, A061247, A199340 - A199349.

Select[FromDigits/@Tuples[{0,1,9},5],PrimeQ] (* Harvey P. Dale, Dec 10 2016 *)

A199329(n=50,show=0,L=[0,1,9])={for(d=1,1e9,my(t,u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,[1+!(L[1]||(i>1&&iM. F. Hasler, Jul 25 2015

A036325 Composite numbers whose prime factors have no digits other than 8 and 9.

Original entry on oeis.org

7921, 704969, 800911, 8001011, 8009021, 8802011, 8810911, 8899021, 62742241, 71281079, 79120021, 80001121, 80982001, 88109911, 88910021, 712089979, 712802869, 783378979, 784171079, 791120021, 791200121, 792012869, 800020021, 800109911, 800901121, 800991011, 809001101, 809811011, 880111121

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020472. - David A. Corneth, Apr 30 2018

			7921 is in the sequence because it's composite and its only prime factor is 89, only having digits 8 or 9. - _David A. Corneth_, Apr 30 2018

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 5375 terms from Robert Israel)
Index entries for sequences related to prime factors.

Cf. A020472, A036302-A036324.

N:= 9: # to get all terms of <= N digits
R:= 10^N: G:= {9}: S:= {1}:
for n from 1 to N-1 do
  G:= map(t -> (t+8*10^n,t+9*10^n), G);
  newprimes:= select(isprime, G);
  for p in newprimes do
    S:= map(s -> seq(s*p^i,i=0..floor(log[p](R/s))), S)
  od
od:
sort(convert(remove(isprime, S minus {1}),list)); # Robert Israel, Apr 30 2018

Sum_{n>=1} 1/a(n) = Product_{p in A020472} (p/(p - 1)) - Sum_{p in A020472} 1/p - 1 = 0.0001296249159... . - Amiram Eldar, May 22 2022

More terms from Robert Israel, Apr 29 2018

A036953 Primes having only {0, 1, 2} as digits.

Original entry on oeis.org

2, 11, 101, 211, 1021, 1201, 2011, 2111, 2221, 10111, 10211, 12011, 12101, 12211, 20011, 20021, 20101, 20201, 21001, 21011, 21101, 21121, 21211, 21221, 22111, 101021, 101111, 101221, 102001, 102101, 102121, 110221, 111121, 111211, 112111

Offset: 1

Patrick De Geest, Jan 04 1999

Number of n-digit terms d(n) = (1, 1, 2, 5, 16, 34, 76, 194, 543, 1469, 4094, 11017, ...); e.g., there are five 4-digit terms: 1021, 1201, 2011, 2111, 2221, hence d(4) = 5. - Zak Seidov, Jun 30 2013

Also, primes in A007089. - M. F. Hasler, Jul 25 2015

Zak Seidov, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
Index to entries for primes with digits in a given set

Subsequence of A107715.
Cf. A036952-A036964.
Cf. A020450 - A020472, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349, A217039, A079651.

Select[FromDigits/@Tuples[{0,1,2},6],PrimeQ] (* Harvey P. Dale, Jul 11 2017 *)

lista(n) = {forprime(p=2, n, if (vecmax(digits(p)) <= 2, print1(p, ", ")))} \\ Michel Marcus, Aug 02 2014

A036953={(n,show=0)->for(d=1,1e9,my(u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,if(i>1,if(iM. F. Hasler, Jul 25 2015

from gmpy2 import digits
from sympy import isprime
[int(digits(n,3)) for n in range(1000) if isprime(int(digits(n,3)))] # Chai Wah Wu, Jul 31 2014

Edited by M. F. Hasler, Jul 25 2015

A199340 Primes having only {0, 3, 4} as digits.

Original entry on oeis.org

3, 43, 433, 443, 3343, 3433, 4003, 30403, 33343, 33403, 34033, 34303, 34403, 40343, 40433, 43003, 43403, 300043, 300343, 304033, 304303, 304433, 330433, 333433, 334043, 334333, 334403, 343303, 343333, 343433, 400033, 403003, 403043, 403433, 430303, 430333

Offset: 1

M. F. Hasler, Nov 05 2011

All terms end in '3'. This could be used to speed up the given program.

A020461 is a subsequence. - Vincenzo Librandi, Jul 23 2015

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries about primes with digits in a given set.

Cf. Primes that contain only the digits (3,4,k): this sequence (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8), A199349 (k=9).
Cf. A020449 - A020472, A199325 - A199329.
Cf. A058429, A058430.

[p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [3, 4, 0]]; // Vincenzo Librandi, Jul 23 2015

Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 4, 0}]=={} &] (* Vincenzo Librandi, Jul 23 2015 *)
Select[FromDigits/@Tuples[{0,3,4},6],PrimeQ] (* Harvey P. Dale, Mar 21 2020 *)
Select[10#+3&/@FromDigits/@Tuples[{0,3,4},5],PrimeQ] (* Harvey P. Dale, May 02 2022 *)

a(n, list=0, L=[0, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))} \\ Syntax updated for current PARI version. - M. F. Hasler, Jul 25 2015

{forprime(p=3,1e6,p%10==3&&!setminus(Set(digits(p)),[3,4])&&print1(p","))} \\ [0] evaluates to false. - M. F. Hasler, Jul 25 2015

A061247 Primes having only {0, 1, 8} as digits.

Original entry on oeis.org

11, 101, 181, 811, 881, 1181, 1801, 1811, 8011, 8081, 8101, 8111, 10111, 10181, 11801, 18181, 80111, 81001, 81101, 81181, 88001, 88801, 88811, 100801, 100811, 101081, 101111, 108011, 108881, 110881, 118081, 118801, 180001, 180181, 180811

Offset: 1

Amarnath Murthy, Apr 23 2001

The intersection with A007500 is listed in A199328. - M. F. Hasler, Nov 05 2011

			a(6) = 1801, 1801 is a prime and consists of only 1, 8 and 0.

Robert Israel, Table of n, a(n) for n = 1..17482

Cf. A061246, A020449-A020472, A199325-A199329.

[NthPrime(n): n in [1..2*10^4] | forall{d: d in Intseq(NthPrime(n)) | d in [0, 1, 8]}]; // Vincenzo Librandi, May 15 2019

N:= 1000: # to get the first N entries
count:= 0:
allowed:= {0,1,8}:
nallowed:= nops(allowed):
subst:= seq(i=allowed[i+1],i=0..nallowed-1);
for d from 1 while count < N do
  for x1 from 1 to nallowed-1 while count < N do
    for t from 0 to nallowed^d-1  while count < N do
      L:= subs(subst,convert(x1*nallowed^d+t,base,nallowed));
      X:= add(L[i]*10^(i-1),i=1..d+1);
      if isprime(X) then
          count:= count+1;
          A[count]:= X;
      fi
od od od:
seq(A[n],n=1..N); # Robert Israel, Apr 20 2014

Select[Prime[Range[50000]],Length[Union[{0,1,8},IntegerDigits[ # ]]] == 3&] (* Stefan Steinerberger, Jun 10 2007 *)
Select[FromDigits/@Tuples[{0,1,8},6],PrimeQ] (* Harvey P. Dale, Jan 12 2016 *)

a(n=50, L=[0, 1, 8], show=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1 && !L[1]), #L]), ispseudoprime(t=vector(d, i, L[v[i]])*u) || next; show && print1(t", "); n-- || return(t)))} \\ M. F. Hasler, Nov 05 2011

Corrected and extended by Stefan Steinerberger, Jun 10 2007

A199349 Primes having only {3, 4, 9} as digits.

Original entry on oeis.org

3, 43, 349, 433, 439, 443, 449, 499, 3343, 3433, 3449, 3499, 3943, 4339, 4349, 4493, 4933, 4943, 4993, 4999, 9343, 9349, 9433, 9439, 9949, 33343, 33349, 33493, 34439, 34499, 34939, 34949, 39343, 39439, 39443, 39499, 43399, 43499, 43933, 43943, 44449, 44939, 49333, 49339, 49393, 49433, 49499, 49939, 49943, 49993

Offset: 1

M. F. Hasler, Nov 05 2011

A020461 and A020466 are subsequences. - Vincenzo Librandi, Jul 30 2015

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries about primes with digits in a given set.

Cf. Primes that contain only the digits (3,4,k): A199340 (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8).

Cf. A020449 - A020472, A199325 - A199329.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [3, 4, 9]]; // Vincenzo Librandi, Jul 30 2015

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {3, 4, 9}]=={} &] (* Vincenzo Librandi, Jul 30 2015 *)
Select[Flatten[Table[FromDigits/@Tuples[{3,4,9},n],{n,5}]],PrimeQ] (* Harvey P. Dale, May 02 2023 *)

a(n, list=0, L=[3,4,9], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vecextract(L,v)*u) || next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))}

A020471 Primes that contain digits 7 and 9 only.

Original entry on oeis.org

7, 79, 97, 797, 977, 997, 77797, 77977, 77999, 79777, 79979, 79997, 79999, 97777, 777977, 777979, 779797, 797977, 799979, 799999, 999979, 7777997, 7779979, 7779997, 7797799, 7797997, 7799797, 7799999, 7977779, 7977797, 7977799, 7977997

Offset: 1

David W. Wilson

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
Index to entries about primes with digits in a given set

Subsequence of A030096.

Cf. A020449 (digits 0 & 1), ..., A020472 (digits 8 & 9).

[p: p in PrimesUpTo(7977997) | Set(Intseq(p)) subset [7,9]]; // Vincenzo Librandi, Jul 28 2012

Flatten[Table[Select[FromDigits/@Tuples[{7,9},n],PrimeQ],{n,7}]] (* Vincenzo Librandi, Jul 28 2012 *)

Edited by M. F. Hasler, Jul 26 2015

A020450 Primes that contain digits 1 and 2 only.

Original entry on oeis.org

2, 11, 211, 2111, 2221, 12211, 21121, 21211, 21221, 22111, 111121, 111211, 112111, 112121, 1111211, 1121221, 1212121, 1212221, 1221221, 2121121, 2211211, 2221111, 11221211, 12111221, 12121121, 12121211, 12122111, 12122221, 12212111, 12222121

Offset: 1

David W. Wilson

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Cf. A020449 (digits 0 & 1), ..., A020472 (digits 8 & 9). [From M. F. Hasler, Mar 18 2010]

Subsequence of A007931.

[p: p in PrimesUpTo(12222121) | Set(Intseq(p)) subset [1, 2]]; // Vincenzo Librandi, Jul 28 2012

Flatten[Table[Select[FromDigits/@Tuples[{1,2},n],PrimeQ],{n,8}]] (* Vincenzo Librandi, Jul 28 2012 *)

for(nd=1,9, forvec(v=vector(nd,i,[49,50-(i==nd && i>1)]), isprime(t=eval(Strchr(Vecsmall(v)))) && print1(t","))) \\ M. F. Hasler, Mar 18 2010

from sympy import primerange
def checkd(a, c):
    b =  set(int(i) for i in set(str(a)))
    return b.issubset(c)
for n in primerange(2, 2000000):
    if checkd(n, [1, 2]):
        print(n)
# Abhiram R Devesh, May 08 2015

A020469 Primes that contain digits 6 and 7 only.

Original entry on oeis.org

7, 67, 677, 67777, 76667, 76777, 666667, 677767, 767677, 777677, 6676667, 6676777, 6677677, 6677767, 6677777, 6766667, 6766777, 6776677, 7666667, 7667677, 7667767, 7766767, 7766777, 7777667, 66666667, 66677777, 66776777, 67667777, 67766767, 67776677, 67776767

Offset: 1

David W. Wilson

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Cf. A020449-A020472.

Flatten[Table[Select[FromDigits/@Tuples[{6,7},n],PrimeQ],{n,8}]] (* Vincenzo Librandi, Jul 27 2012 *)

from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    yield 7
    for d in count(2):
        for first in product("67", repeat=d-1):
            t = int("".join(first) + "7")
            if isprime(t): yield t
print(list(islice(agen(), 31))) # Michael S. Branicky, Nov 15 2022

cp's OEIS Frontend

A199325 Primes having only {0, 1, 5} as digits.

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A199329 Primes having only {0, 1, 9} as digits.

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A036325 Composite numbers whose prime factors have no digits other than 8 and 9.

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A036953 Primes having only {0, 1, 2} as digits.

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A199340 Primes having only {0, 3, 4} as digits.

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A061247 Primes having only {0, 1, 8} as digits.

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A199349 Primes having only {3, 4, 9} as digits.

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