A260829 -id:A260829 - 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

A386077 Primes having only {0, 5, 6, 7} as digits.

Original entry on oeis.org

5, 7, 67, 557, 577, 607, 677, 757, 5077, 5507, 5557, 5657, 6007, 6067, 6577, 6607, 7057, 7507, 7577, 7607, 7757, 50077, 50707, 50767, 50777, 55057, 55667, 56767, 57077, 57557, 57667, 60077, 60607, 60757, 65557, 65657, 65677, 65707, 65777, 66067, 67057, 67567

Offset: 1

Jason Bard, Jul 16 2025

Supersequence of A260827, A260829, A385770.

Cf. A000040, A030432, A385776.

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

Select[FromDigits /@ Tuples[{0, 5, 6, 7}, n], PrimeQ]

primes_with(, 1, [0, 5, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("0567"), 41))) # uses function/imports in A385776

A386129 Primes having only {1, 5, 6, 7} as digits.

Original entry on oeis.org

5, 7, 11, 17, 61, 67, 71, 151, 157, 167, 557, 571, 577, 617, 661, 677, 751, 757, 761, 1117, 1151, 1171, 1511, 1567, 1571, 1657, 1667, 1777, 5167, 5171, 5557, 5651, 5657, 5711, 5717, 6151, 6551, 6571, 6577, 6661, 6761, 7151, 7177, 7517, 7561, 7577, 7717, 7757

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A260828, A260829, A260891, A385779.

Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{1, 5, 6, 7}, n], PrimeQ], {n, 7}]]

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

print(list(islice(primes_with("1567"), 41))) # uses function/imports in A385776

A386160 Primes having only {2, 5, 6, 7} as digits.

Original entry on oeis.org

2, 5, 7, 67, 227, 257, 277, 557, 577, 677, 727, 757, 2267, 2557, 2657, 2677, 2767, 2777, 5227, 5527, 5557, 5657, 6257, 6277, 6577, 7577, 7727, 7757, 22277, 22567, 22727, 22777, 25577, 25657, 25667, 26227, 26267, 26557, 26627, 26777, 27277, 27527, 27767, 52267

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A214705, A260829, A385787.

Cf. A000040, A030432, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{2, 5, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 5, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("2567"), 41))) # uses function/imports in A385776

A386178 Primes having only {3, 5, 6, 7} as digits.

Original entry on oeis.org

3, 5, 7, 37, 53, 67, 73, 337, 353, 367, 373, 557, 563, 577, 653, 673, 677, 733, 757, 773, 3373, 3533, 3557, 3637, 3673, 3677, 3733, 3767, 5333, 5557, 5563, 5573, 5653, 5657, 5737, 6337, 6353, 6367, 6373, 6553, 6563, 6577, 6637, 6653, 6673, 6733, 6737, 6763, 7333

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A087363, A260225, A260380, A260829.

Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{3, 5, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [3, 5, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("3567"), 41))) # uses function/imports in A385776

A386188 Primes having only {4, 5, 6, 7} as digits.

Original entry on oeis.org

5, 7, 47, 67, 457, 467, 547, 557, 577, 647, 677, 757, 4447, 4457, 4547, 4567, 4657, 5477, 5557, 5647, 5657, 6547, 6577, 7457, 7477, 7547, 7577, 7757, 44647, 44657, 44777, 45557, 45667, 45677, 45757, 45767, 46447, 46457, 46477, 46567, 46747, 46757, 47657, 47777

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A217039, A260829, A385794.

Cf. A000040, A030432, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{4, 5, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 5, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("4567"), 41))) # uses function/imports in A385776

A386196 Primes having only {5, 6, 7, 8} as digits.

Original entry on oeis.org

5, 7, 67, 557, 577, 587, 677, 757, 787, 857, 877, 887, 5557, 5657, 5857, 5867, 6577, 6857, 7577, 7687, 7757, 7867, 7877, 8677, 8867, 8887, 55667, 55787, 56687, 56767, 56857, 57557, 57587, 57667, 57787, 58567, 58657, 58687, 58757, 58787, 65557, 65587, 65657, 65677

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A260829, A260830, A385799.

Cf. A000040, A030432, A106111, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{5, 6, 7, 8}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [5, 6, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("5678"), 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

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

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A386077 Primes having only {0, 5, 6, 7} as digits.

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A386129 Primes having only {1, 5, 6, 7} as digits.

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A386160 Primes having only {2, 5, 6, 7} as digits.

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A386178 Primes having only {3, 5, 6, 7} as digits.

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A386188 Primes having only {4, 5, 6, 7} as digits.

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A386196 Primes having only {5, 6, 7, 8} as digits.

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Magma

Mathematica

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Python

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

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