A385770 -id:A385770 - cp's OEIS frontend

A386051 Primes having only {0, 2, 6, 7} as digits.

2, 7, 67, 227, 277, 607, 677, 727, 2027, 2207, 2267, 2677, 2707, 2767, 2777, 6007, 6067, 6277, 6607, 7027, 7207, 7607, 7727, 20627, 20707, 22027, 22067, 22277, 22727, 22777, 26227, 26267, 26627, 26777, 27067, 27077, 27277, 27767, 60077, 60607, 60727, 62207, 62627

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A261267, A385770, A385787.

Cf. A000040, A030432, A385776.

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

Select[FromDigits /@ Tuples[{0, 2, 6, 7}, n], PrimeQ]

primes_with(, 1, [0, 2, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("0267"), 41))) # uses function/imports in A385776

A386065 Primes having only {0, 3, 6, 7} as digits.

Original entry on oeis.org

3, 7, 37, 67, 73, 307, 337, 367, 373, 607, 673, 677, 733, 773, 3037, 3067, 3307, 3373, 3607, 3637, 3673, 3677, 3733, 3767, 6007, 6037, 6067, 6073, 6337, 6367, 6373, 6607, 6637, 6673, 6703, 6733, 6737, 6763, 7307, 7333, 7603, 7607, 7673, 7703, 30307, 30367, 30637

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A260378, A260380, A385770.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 6, 7]];

Select[FromDigits /@ Tuples[{0, 3, 6, 7}, n], PrimeQ]

primes_with(, 1, [0, 3, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("0367"), 41))) # uses function/imports in A385776

A386072 Primes having only {0, 4, 6, 7} as digits.

Original entry on oeis.org

7, 47, 67, 467, 607, 647, 677, 4007, 4447, 6007, 6047, 6067, 6607, 7477, 7607, 44647, 44777, 46447, 46477, 46747, 47407, 47777, 60077, 60607, 60647, 64007, 64067, 64667, 64747, 66047, 66067, 66467, 67447, 67477, 67607, 67777, 70067, 70607, 70667, 74047, 74077

Offset: 1

Jason Bard, Jul 16 2025

Subsequence of A030432.
Supersequence of A384449, A385770, A385794.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 4, 6, 7]];

Select[FromDigits /@ Tuples[{0, 4, 6, 7}, n], PrimeQ]

primes_with(, 1, [0, 4, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("0467"), 41))) # uses function/imports in A385776

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

A386082 Primes having only {0, 6, 7, 8} as digits.

Original entry on oeis.org

7, 67, 607, 677, 787, 877, 887, 6007, 6067, 6607, 7607, 7687, 7867, 7877, 8087, 8677, 8707, 8807, 8867, 8887, 60077, 60607, 60887, 66067, 66877, 67607, 67777, 67807, 67867, 68087, 68687, 68767, 68777, 70067, 70607, 70667, 70687, 70867, 70877, 76607, 76667, 76777

Offset: 1

Jason Bard, Jul 16 2025

Subsequence of A030432.
Supersequence of A385770, A385771, A385799.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 6, 7, 8]];

Select[FromDigits /@ Tuples[{0, 6, 7, 8}, n], PrimeQ]

primes_with(, 1, [0, 6, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("0678"), 41))) # uses function/imports in A385776

A386083 Primes having only {0, 6, 7, 9} as digits.

Original entry on oeis.org

7, 67, 79, 97, 607, 677, 709, 769, 797, 907, 967, 977, 997, 6007, 6067, 6079, 6607, 6679, 6709, 6779, 6907, 6967, 6977, 6997, 7069, 7079, 7607, 7669, 7699, 7907, 9007, 9067, 9677, 9679, 9697, 9767, 9769, 9907, 9967, 60077, 60607, 60679, 60779, 66067, 66697, 66797

Offset: 1

Jason Bard, Jul 16 2025

Supersequence of A261181, A261184, A385770.

Cf. A000040, A385776.

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

Select[FromDigits /@ Tuples[{0, 6, 7, 9}, n], PrimeQ]

primes_with(, 1, [0, 6, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("0679"), 41))) # uses function/imports in A385776

A386004 Primes whose digit set intersects the odd digits in at most one element and intersects the even digits in at most two elements.

Original entry on oeis.org

2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 181, 211, 223, 227, 229, 233, 241, 263, 269, 277, 281, 283, 383, 401, 409, 421, 433, 443, 449, 461, 463, 467, 487, 499, 601, 607, 641, 643, 647, 661, 677, 683, 727, 787, 809, 811, 821, 823, 827, 829, 863

Offset: 1

Jean-Marc Rebert, Jul 14 2025

From David A. Corneth, Jul 14 2025: (Start)
Terms can have at most three distinct digits.
Terms > 5 cannot have a digit 5. Proof: Terms > 5 are odd as they are prime. They cannot have a last digit 5. So if they have a digit 5 then they have at least two distinct odd digits contradicting the sequence definition of having at most one odd digit. (End)

			101 is a term because it is prime and its digit set is {0, 1} — containing at most one odd digit and no more than two distinct even digits.
1021 is a term because it is prime and its digit set is {0,1,2} — containing at most one odd digit and no more than two distinct even digits.

Cf. A000040, A020469, A020450, A020457, A020460, A385770.

Select[Prime[Range[150]],Length[Intersection[d=IntegerDigits[#],{1,3,5,7,9}]]<=1 && Length[Intersection[d,{0,2,4,6,8}]]<=2 &] (* Stefano Spezia, Jul 14 2025 *)

is(n) = if(!isprime(n), return(0)); my(s=Set(digits(n)), odd=0); if(#s>3,return(0)); odd=sum(i=1, #s ,bitand(s[i], 1)); if(odd > 1, return(0)); if(#s-odd > 2, return(0)); 1 \\ David A. Corneth, Jul 14 2025

cp's OEIS Frontend

A386051 Primes having only {0, 2, 6, 7} as digits.

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A386065 Primes having only {0, 3, 6, 7} as digits.

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A386072 Primes having only {0, 4, 6, 7} as digits.

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

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A386082 Primes having only {0, 6, 7, 8} as digits.

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Magma

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A386083 Primes having only {0, 6, 7, 9} as digits.

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Magma

Mathematica

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A386004 Primes whose digit set intersects the odd digits in at most one element and intersects the even digits in at most two elements.

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