A030096 -id:A030096 - cp's OEIS frontend

A020462 Primes that contain digits 3 and 5 only.

3, 5, 53, 353, 3533, 5333, 33353, 33533, 35353, 35533, 53353, 55333, 333533, 353333, 533353, 535333, 3335533, 3353333, 3353533, 3355553, 3533533, 3553553, 3555353, 5333353, 5333533, 5353553, 5533553, 33335333, 33555553, 35535553, 35553533, 53355353, 53533553

Offset: 1

David W. Wilson

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

Subsequence of A030096.

sort(convert(`union`(seq(select(isprime,map(t -> 3*(10^d-1)/9 + 2*add(10^(s-1),s=t),combinat:-powerset(d))),d=0..10)),list)); # Robert Israel, Jul 21 2015

Flatten[Table[Select[FromDigits/@Tuples[{3,5},n],PrimeQ],{n,8}]] (* Vincenzo Librandi, Jul 27 2012 *)

from gmpy2 import is_prime, mpz
from itertools import product
A020462_list = [int(''.join(x)) for n in range(1,10) for x in product('35',repeat=n) if is_prime(mpz(''.join(x)))] # Chai Wah Wu, Jul 21 2015

A260831 Primes having only {5, 7, 9} as digits.

Original entry on oeis.org

5, 7, 59, 79, 97, 557, 577, 599, 757, 797, 977, 997, 5557, 5779, 7559, 7577, 7757, 7759, 55579, 55799, 55997, 57557, 57559, 57977, 59557, 59779, 59797, 59957, 59999, 75557, 75577, 75797, 75979, 75997, 77557, 77797, 77977, 77999, 79559, 79579, 79757, 79777

Offset: 1

Vincenzo Librandi, Aug 03 2015

A020467, A020468 and A020471 are subsequences.

Subsequence of A030096.

Alois P. Heinz, 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

Cf. similar sequences listed in A260827.

Cf. A000040, A020467, A020468, A020471, A030096.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [5, 7, 9]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 7, 9}] == {} &]

A020467 Primes that contain digits 5 and 7 only.

Original entry on oeis.org

5, 7, 557, 577, 757, 5557, 7577, 7757, 57557, 75557, 75577, 77557, 555557, 575557, 575777, 577757, 757577, 775757, 775777, 5555777, 5557757, 5575777, 5577577, 5755577, 5775557, 5777557, 7575577, 7577777, 55555777, 55575757, 55755757, 55757777, 57557557

Offset: 1

David W. Wilson

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

Subsequence of A030096, A260827-A260831, and A284380.

[p: p in PrimesUpTo(55755757 ) | Set(Intseq(p)) subset [5, 7]];// Vincenzo Librandi, Jul 27 2012

Flatten[Table[Select[FromDigits/@Tuples[{5,7},n],PrimeQ],{n,8}]]

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
  n, digits, alst = 0, 1, []
  while len(alst) < terms:
    mpstr = "".join(d*digits for d in "57")
    for mp in multiset_permutations(mpstr, digits):
      t = int("".join(mp))
      if isprime(t): alst.append(t)
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(33)) # Michael S. Branicky, May 07 2021

A260828 Primes having only {1, 5, 7} as digits.

Original entry on oeis.org

5, 7, 11, 17, 71, 151, 157, 557, 571, 577, 751, 757, 1117, 1151, 1171, 1511, 1571, 1777, 5171, 5557, 5711, 5717, 7151, 7177, 7517, 7577, 7717, 7757, 11117, 11171, 11177, 11551, 11717, 11777, 15511, 15551, 17117, 17551, 51151, 51157, 51511, 51517, 51551, 51577

Offset: 1

Vincenzo Librandi, Aug 02 2015

Alois P. Heinz, 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 A030096. A020453, A020455 and A020467 are subsequences.
Cf. similar sequences listed in A260827.
Cf. A000040.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1,5,7]];

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 5, 7}] == {} &]

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
  n, digits, alst = 0, 1, []
  while len(alst) < terms:
    mpstr = "".join(d*digits for d in "157")
    for mp in multiset_permutations(mpstr, digits):
      t = int("".join(mp))
      if isprime(t): alst.append(t)
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(44)) # Michael S. Branicky, May 07 2021

A051416 Primes whose digits are composite; primes having only {4, 6, 8, 9} as digits.

Original entry on oeis.org

89, 449, 499, 4649, 4889, 4969, 4999, 6449, 6469, 6689, 6869, 6899, 6949, 8669, 8689, 8699, 8849, 8969, 8999, 9649, 9689, 9949, 44449, 44699, 46489, 46499, 46649, 46889, 48449, 48649, 48869, 48889, 48989, 49499, 49669, 49999, 64489, 64499, 64849, 64969, 66449

Offset: 1

G. L. Honaker, Jr., Jan 17 2000

Primes formed by using only digits 4, 6, 8, 9. Of course, all the terms of this sequence end with 9. - Bernard Schott, Jan 31 2019

			89 is the smallest composite-digit prime and also the only composite-digit prime whose digits are distinct. - _Bernard Schott_, Jan 31 2019

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Chris Caldwell, The Prime Glossary, Composite number
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 89
Index to entries for primes with digits in a given set

Cf. A019546 (with prime digits), A030096 (with odd digits), A061246 (with square digits), A061371 (composite numbers with prime digits).

Subsequence of A061372 and of A152313.

Select[Prime@Range[6500], Intersection[IntegerDigits[ # ], {0, 1, 2, 3, 5, 7}] == {} & ] (* Ray Chandler, Mar 04 2007 *)
With[{c = {4, 6, 8, 9}}, Array[Select[Map[FromDigits@ Append[#, 9] &, Tuples[c, {#}]], PrimeQ] &, 4]] // Flatten (* Michael De Vlieger, Feb 02 2019 *)

Extended by Ray Chandler, Mar 04 2007

A108386 Primes p such that p's set of distinct digits is {1,3,7,9}.

Original entry on oeis.org

1973, 3719, 3917, 7193, 9137, 9173, 9371, 13397, 13799, 13997, 17393, 17939, 19373, 19379, 19739, 19793, 19937, 19973, 31379, 31397, 31793, 31799, 31973, 33179, 33791, 37139, 37199, 37991, 39317, 39371, 39719, 39791, 39971, 71339, 71399

Offset: 1

Rick L. Shepherd, Jun 01 2005

The digits in {1,3,7,9} are the possible ending digits of multidigit primes. [Corrected by Lekraj Beedassy, Apr 04 2009]

Subsequence of A091633. - Michel Marcus, Jun 08 2014

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A108382 ({1, 3, 7}), A108383 ({1, 3, 9}), A108384 ({1, 7, 9}), A108385 ({3, 7, 9}), A030096 (Primes whose digits are all odd).

A260379 Primes having only {1, 3, 7} as digits.

Original entry on oeis.org

3, 7, 11, 13, 17, 31, 37, 71, 73, 113, 131, 137, 173, 311, 313, 317, 331, 337, 373, 733, 773, 1117, 1171, 1373, 1733, 1777, 3137, 3313, 3331, 3371, 3373, 3733, 7177, 7331, 7333, 7717, 11113, 11117, 11131, 11171, 11173, 11177, 11311, 11317, 11717, 11731, 11777

Offset: 1

Vincenzo Librandi, Jul 24 2015

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

Subsequence of A030096 and A155055. A020451, A020455, and A020463 are subsequences.
Cf. similar sequences listed in A260378.
Cf. A000040, A020451, A020455, A020463.

[p: p in PrimesUpTo(2*10^4) | Set(Intseq(p)) subset [1, 3, 7]];

Select[Prime[Range[2 10^3]], Complement[IntegerDigits[#], {1, 3, 7}]=={} &]

A260893 Primes having only {1, 7, 9} as digits.

Original entry on oeis.org

7, 11, 17, 19, 71, 79, 97, 179, 191, 197, 199, 719, 797, 911, 919, 971, 977, 991, 997, 1117, 1171, 1777, 1979, 1997, 1999, 7177, 7717, 7919, 9199, 9719, 9791, 11117, 11119, 11171, 11177, 11197, 11717, 11719, 11777, 11779, 11971, 17117, 17191, 17791, 17911

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020455, A020457 and A020471 are subsequences.

Subsequence of A030096.

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

Cf. similar sequences listed in A260889.

Cf. A000040, A020455, A020457, A020471, A030096.

[p: p in PrimesUpTo(3*10^4) | Set(Intseq(p)) subset [1, 7, 9]];

Select[Prime[Range[3 10^3]], Complement[IntegerDigits[#], {1, 7, 9}] == {}&]

A260224 Primes having only {1, 3, 5} as digits.

Original entry on oeis.org

3, 5, 11, 13, 31, 53, 113, 131, 151, 311, 313, 331, 353, 1151, 1153, 1511, 1531, 1553, 3313, 3331, 3511, 3533, 5113, 5153, 5333, 5351, 5531, 11113, 11131, 11311, 11351, 11353, 11551, 13151, 13313, 13331, 13513, 13553, 15131, 15313, 15331, 15511, 15551

Offset: 1

Vincenzo Librandi, Jul 21 2015

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

Subsequence of A030096. A004022, A020451, A020453, and A020462 are subsequences.
Cf. similar sequences listed in A260223.
Cf. A020451, A020453, A020462, A385776.

[p: p in PrimesUpTo(40000) | Set(Intseq(p)) subset [3, 5, 1]];

Select[Prime[Range[3 10^3]], Complement[IntegerDigits[#], {3, 5, 1}]=={} &]
Select[Flatten[Table[FromDigits/@Tuples[{1,3,5},n],{n,5}]],PrimeQ] (* Harvey P. Dale, Mar 03 2020 *)

from gmpy2 import is_prime, mpz
from itertools import product
A260224_list = [int(''.join(x)) for n in range(1,10) for x in product('135',repeat=n) if is_prime(mpz(''.join(x)))] # Chai Wah Wu, Jul 21 2015

A272381 Primes p == 1 (mod 3) for which A261029(10*p) = 2.

Original entry on oeis.org

7, 13, 19, 31, 37, 73

Offset: 1

Vladimir Shevelev, Apr 28 2016

Peter J. C. Moses did not find any term > 73. The author proved that the sequence is full.

Subsequence of A030096.

Cf. A261029.

cp's OEIS Frontend

A020462 Primes that contain digits 3 and 5 only.

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A260831 Primes having only {5, 7, 9} as digits.

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Magma

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A020467 Primes that contain digits 5 and 7 only.

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Magma

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A260828 Primes having only {1, 5, 7} as digits.

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Magma

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A051416 Primes whose digits are composite; primes having only {4, 6, 8, 9} as digits.

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Mathematica

Extensions

A108386 Primes p such that p's set of distinct digits is {1,3,7,9}.

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A260379 Primes having only {1, 3, 7} as digits.

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Magma

Mathematica

A260893 Primes having only {1, 7, 9} as digits.

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Magma

Mathematica

A260224 Primes having only {1, 3, 5} as digits.

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