A020467 -id:A020467 - cp's OEIS frontend

A260827 Primes having only {0, 5, 7} as digits.

5, 7, 557, 577, 757, 5077, 5507, 5557, 7057, 7507, 7577, 7757, 50077, 50707, 50777, 55057, 57077, 57557, 70507, 75557, 75577, 75707, 77557, 500057, 500777, 505777, 507077, 507557, 507757, 550007, 550577, 550757, 555077, 555557, 555707, 557057, 570077, 575077

Offset: 1

Vincenzo Librandi, Aug 01 2015

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

A020467 is a subsequence.
Cf. Primes that contain only the digits (k,5,7): this sequence (k=0), A260828 (k=1), A214705 (k=2), A087363 (k=3), A217039 (k=4), A260829 (k=6), A260830 (k=8), A260831 (k=9).
Cf. A000040.

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0,5,7]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {0, 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 "057")
    for mp in multiset_permutations(mpstr, digits):
      if mp[0] == "0": continue
      t = int("".join(mp))
      if isprime(t): alst.append(t)
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(38)) # Michael S. Branicky, May 07 2021

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}] == {} &]

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

A260829 Primes having only {5, 6, 7} as digits.

Original entry on oeis.org

5, 7, 67, 557, 577, 677, 757, 5557, 5657, 6577, 7577, 7757, 55667, 56767, 57557, 57667, 65557, 65657, 65677, 65777, 67567, 67577, 67757, 67777, 75557, 75577, 75767, 76667, 76757, 76777, 77557, 555557, 555677, 555767, 557567, 565567, 565667, 566557, 566567

Offset: 1

Vincenzo Librandi, Aug 02 2015

A020467 and A020469 are subsequences.

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. A020467, A020469.

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [5,6,7]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 6, 7}] == {} &]

A260830 Primes having only {5, 7, 8} as digits.

Original entry on oeis.org

5, 7, 557, 577, 587, 757, 787, 857, 877, 887, 5557, 5857, 7577, 7757, 7877, 8887, 55787, 57557, 57587, 57787, 58757, 58787, 75557, 75577, 75787, 77557, 77587, 78577, 78787, 78857, 78877, 78887, 85577, 87557, 87587, 87877, 87887, 555557, 555857, 557857, 558587

Offset: 1

Vincenzo Librandi, Aug 02 2015

A020467 and A020470 are subsequences.

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. A020467, A020470.

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [5,7,8]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 7, 8}] == {} &]
Select[Flatten[Table[FromDigits/@Tuples[{5,7,8},n],{n,6}]],PrimeQ] (* Harvey P. Dale, Oct 06 2017 *)

A284380 Numbers k with digits 5 and 7 only.

Original entry on oeis.org

5, 7, 55, 57, 75, 77, 555, 557, 575, 577, 755, 757, 775, 777, 5555, 5557, 5575, 5577, 5755, 5757, 5775, 5777, 7555, 7557, 7575, 7577, 7755, 7757, 7775, 7777, 55555, 55557, 55575, 55577, 55755, 55757, 55775, 55777, 57555, 57557, 57575, 57577, 57755, 57757

Offset: 1

Jaroslav Krizek, Mar 28 2017

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Prime terms are in A020467.

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), this sequence (k = 7), A284381 (k = 8), A284382 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 7}];

Join @@ ((FromDigits /@ Tuples[{5, 7}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)

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):
      alst.append(int("".join(mp)))
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(44)) # Michael S. Branicky, May 07 2021

A036320 Composite numbers whose prime factors contain no digits other than 5 and 7.

Original entry on oeis.org

25, 35, 49, 125, 175, 245, 343, 625, 875, 1225, 1715, 2401, 2785, 2885, 3125, 3785, 3899, 4039, 4375, 5299, 6125, 8575, 12005, 13925, 14425, 15625, 16807, 18925, 19495, 20195, 21875, 26495, 27293, 27785, 28273, 30625, 37093, 37885, 38785

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020467. - David A. Corneth, Oct 09 2020

David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for sequences related to prime factors.

Cf. A003595, A020467, A036302-A036325.

Sum_{n>=1} 1/a(n) = Product_{p in A020467} (p/(p - 1)) - Sum_{p in A020467} 1/p - 1 = 0.1179595738... . - Amiram Eldar, May 22 2022

A036946 Smallest n-digit prime containing only the digits 5 and 7, or 0 if no such prime exists.

Original entry on oeis.org

5, 0, 557, 5557, 57557, 555557, 5555777, 55555777, 555557557, 5555555557, 55555555777, 555555575557, 5555555757757, 55555555575757, 555555555555557, 5555555555557577, 55555555555777777, 555555555557557757, 5555555555555557577, 55555555555575755777

Offset: 1

Patrick De Geest, Jan 04 1999

Jinyuan Wang, Table of n, a(n) for n = 1..500

Cf. A020467, A036229, A036320.

Flatten[Join[{5,0},Table[Select[FromDigits/@(Join[#,{7}]&/@Tuples[ {5,7},n]), PrimeQ,1],{n,2,20}]]] (* Harvey P. Dale, Mar 08 2013 *)

More terms from Harvey P. Dale, Mar 08 2013

A386351 Primes without {5, 7} as digits.

Original entry on oeis.org

2, 3, 11, 13, 19, 23, 29, 31, 41, 43, 61, 83, 89, 101, 103, 109, 113, 131, 139, 149, 163, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 263, 269, 281, 283, 293, 311, 313, 331, 349, 383, 389, 401, 409, 419, 421, 431, 433, 439, 443, 449, 461, 463, 491, 499

Offset: 1

Jason Bard, Jul 20 2025

Intersection of A038613 and A038615.

Cf. A000040, A020467, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 3, 4, 6, 8, 9]];

Select[Prime[Range[120]], DigitCount[#, 10, 5] == 0 && DigitCount[#, 10, 7] == 0 &]

primes_with(, 1, [0, 1, 2, 3, 4, 6, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("01234689"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A260827 Primes having only {0, 5, 7} as digits.

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

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

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A260829 Primes having only {5, 6, 7} as digits.

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A260830 Primes having only {5, 7, 8} as digits.

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A284380 Numbers k with digits 5 and 7 only.

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A036320 Composite numbers whose prime factors contain no digits other than 5 and 7.

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A036946 Smallest n-digit prime containing only the digits 5 and 7, or 0 if no such prime exists.

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A386351 Primes without {5, 7} as digits.

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