A260831 -id:A260831 - 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

A261181 Primes that contain only the digits (0, 7, 9).

Original entry on oeis.org

7, 79, 97, 709, 797, 907, 977, 997, 7079, 7907, 9007, 9907, 70009, 70079, 70099, 70709, 70979, 70997, 70999, 77797, 77977, 77999, 79777, 79907, 79979, 79997, 79999, 90007, 90709, 90907, 90977, 90997, 97007, 97777, 99079, 99707, 99709, 99907, 700079

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020471 is a subsequence.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)

Cf. Primes that contain only the digits (k,7,9): this sequence (k=0), A260893 (k=1), A261182 (k=2), A260382 (k=3), A261183 (k=4), A260831 (k=5), A261184 (k=6), A106110 (k=8).

Cf. A000040, A020471.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [0, 7, 9]];

Select[Prime[Range[6 10^4]], Complement[IntegerDigits[#], {0, 7, 9}] == {} &]
Select[FromDigits/@Tuples[{0,7,9},6],PrimeQ] (* Harvey P. Dale, Aug 09 2024 *)

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

A386080 Primes having only {0, 5, 7, 9} as digits.

Original entry on oeis.org

5, 7, 59, 79, 97, 509, 557, 577, 599, 709, 757, 797, 907, 977, 997, 5009, 5059, 5077, 5099, 5507, 5557, 5779, 7057, 7079, 7507, 7559, 7577, 7757, 7759, 7907, 9007, 9059, 9907, 50077, 50599, 50707, 50777, 50909, 50957, 55009, 55057, 55079, 55579, 55799, 55997

Offset: 1

Jason Bard, Jul 16 2025

Supersequence of A260827, A260831, A261181, A385769.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 5, 7, 9]];

Select[FromDigits /@ Tuples[{0, 5, 7, 9}, n], PrimeQ]

primes_with(, 1, [0, 5, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("0579"), 41))) # uses function/imports in A385776

A386133 Primes having only {1, 5, 7, 9} as digits.

Original entry on oeis.org

5, 7, 11, 17, 19, 59, 71, 79, 97, 151, 157, 179, 191, 197, 199, 557, 571, 577, 599, 719, 751, 757, 797, 911, 919, 971, 977, 991, 997, 1117, 1151, 1171, 1511, 1559, 1571, 1579, 1597, 1759, 1777, 1951, 1979, 1997, 1999, 5119, 5171, 5179, 5197, 5519, 5557, 5591

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A260828, A260831, A260893, A385781.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 5, 7, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 5, 7, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 5, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("1579"), 41))) # uses function/imports in A385776

A386163 Primes having only {2, 5, 7, 9} as digits.

Original entry on oeis.org

2, 5, 7, 29, 59, 79, 97, 227, 229, 257, 277, 557, 577, 599, 727, 757, 797, 929, 977, 997, 2297, 2557, 2579, 2729, 2777, 2797, 2927, 2957, 2999, 5227, 5279, 5297, 5527, 5557, 5779, 5927, 7229, 7297, 7529, 7559, 7577, 7727, 7757, 7759, 7927, 9227, 9257, 9277, 9929

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A214705, A260831, A261182, A385786.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 5, 7, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 5, 7, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 5, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("2579"), 41))) # uses function/imports in A385776

A386182 Primes having only {3, 5, 7, 9} as digits.

Original entry on oeis.org

3, 5, 7, 37, 53, 59, 73, 79, 97, 337, 353, 359, 373, 379, 397, 557, 577, 593, 599, 733, 739, 757, 773, 797, 937, 953, 977, 997, 3359, 3373, 3533, 3539, 3557, 3559, 3593, 3733, 3739, 3779, 3793, 3797, 5333, 5393, 5399, 5557, 5573, 5737, 5779, 5939, 5953, 7333

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A087363, A260227, A260382, A260831.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [3, 5, 7, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{3, 5, 7, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [3, 5, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("3579"), 41))) # uses function/imports in A385776

A386191 Primes having only {4, 5, 7, 9} as digits.

Original entry on oeis.org

5, 7, 47, 59, 79, 97, 449, 457, 479, 499, 547, 557, 577, 599, 757, 797, 947, 977, 997, 4447, 4457, 4547, 4549, 4597, 4759, 4799, 4957, 4999, 5449, 5477, 5479, 5557, 5749, 5779, 7457, 7459, 7477, 7499, 7547, 7549, 7559, 7577, 7757, 7759, 7949, 9479, 9497, 9547

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A217039, A260831, A261183, A385793.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 5, 7, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 5, 7, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 5, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("4579"), 41))) # uses function/imports in A385776

A386197 Primes having only {5, 6, 7, 9} as digits.

Original entry on oeis.org

5, 7, 59, 67, 79, 97, 557, 569, 577, 599, 659, 677, 757, 769, 797, 967, 977, 997, 5557, 5569, 5657, 5659, 5669, 5779, 6569, 6577, 6599, 6659, 6679, 6779, 6959, 6967, 6977, 6997, 7559, 7577, 7669, 7699, 7757, 7759, 9677, 9679, 9697, 9767, 9769, 9967, 55579, 55667

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A260829, A260831, A261184, A385797.

Cf. A000040, A106111, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [5, 6, 7, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{5, 6, 7, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [5, 6, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("5679"), 41))) # uses function/imports in A385776

A386199 Primes having only {5, 7, 8, 9} as digits.

Original entry on oeis.org

5, 7, 59, 79, 89, 97, 557, 577, 587, 599, 757, 787, 797, 857, 859, 877, 887, 977, 997, 5557, 5779, 5857, 5879, 5897, 5987, 7559, 7577, 7589, 7757, 7759, 7789, 7877, 7879, 8597, 8599, 8779, 8887, 8999, 9587, 9787, 9857, 9859, 9887, 55579, 55589, 55787, 55799, 55889

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A106110, A260830, A260831, A385798.

Cf. A000040, A106111, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [5, 7, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{5, 7, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [5, 7, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("5789"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

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

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A261181 Primes that contain only the digits (0, 7, 9).

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A020467 Primes that contain digits 5 and 7 only.

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A386080 Primes having only {0, 5, 7, 9} as digits.

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A386133 Primes having only {1, 5, 7, 9} as digits.

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A386163 Primes having only {2, 5, 7, 9} as digits.

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A386182 Primes having only {3, 5, 7, 9} as digits.

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A386191 Primes having only {4, 5, 7, 9} as digits.

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