A385776 -id:A385776 - cp's OEIS frontend

A385768 Primes having only {0, 4, 9} as digits.

409, 449, 499, 4049, 4099, 4409, 4909, 4999, 9049, 9949, 40009, 40099, 40499, 40949, 44449, 44909, 49009, 49409, 49499, 49999, 90499, 94009, 94049, 94099, 94949, 94999, 99409, 400009, 400409, 400949, 404009, 404099, 404449, 409099, 409499, 409909, 409999

Offset: 1

Jason Bard, Jul 09 2025

			4099 is a term because it is prime, and it only contains {0,4,9}.

Cf. A000040, A020466, A385776.

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

Select[FromDigits/@Tuples[{0,4,9},5],PrimeQ]

primes_with(, 1, [0, 4, 9]) \\ uses function in A385776

print(list(islice(primes_with("049"), 41))) # uses function/imports in A385776

A385800 Primes having only {6, 8, 9} as digits.

Original entry on oeis.org

89, 6689, 6869, 6899, 8669, 8689, 8699, 8969, 8999, 9689, 66889, 68669, 68699, 68899, 69899, 86689, 86869, 86969, 88969, 89669, 89689, 89899, 89989, 96989, 98669, 98689, 98869, 98899, 98999, 99689, 99989, 666889, 666989, 668699, 668869, 668989, 668999, 669689, 669869

Offset: 1

Jason Bard, Jul 14 2025

Subsequence of A030431, A106111.
Supersequence of A020472.
Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{6, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [6, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("689"), 41))) # uses function/imports in A385776

A214704 Primes that contain only the digits (2, 3, 7).

Original entry on oeis.org

2, 3, 7, 23, 37, 73, 223, 227, 233, 277, 337, 373, 727, 733, 773, 2237, 2273, 2333, 2377, 2777, 3323, 3373, 3727, 3733, 7237, 7333, 7723, 7727, 22273, 22277, 22727, 22777, 23227, 23327, 23333, 23773, 27277, 27337, 27733, 27737, 27773, 32233, 32237, 32323

Offset: 1

Vincenzo Librandi, Jul 28 2012

The digits are prime numbers excluding 5.

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

Subsequence of A019546.
Cf. A087363 (primes with only prime digits excluding 2).
Cf. A385776 (main sequence for primes containing three distinct digits).

[p: p in PrimesUpTo(80000) | Set(Intseq(p)) subset [2,3,7]];

Flatten[Table[Select[FromDigits/@Tuples[{2,3,7},n],PrimeQ],{n,6}]]

A261182 Primes having only {2, 7, 9} as digits.

Original entry on oeis.org

2, 7, 29, 79, 97, 227, 229, 277, 727, 797, 929, 977, 997, 2297, 2729, 2777, 2797, 2927, 2999, 7229, 7297, 7727, 7927, 9227, 9277, 9929, 22229, 22277, 22279, 22727, 22777, 27277, 27299, 27779, 27799, 27997, 29297, 29927, 72227, 72229, 72277, 72727, 72797

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020459, A020460 and A020471 are subsequences.

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

Cf. similar sequences listed in A261181.

Cf. A000040, A020459, A020460, A020471, A385776.

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

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {2, 7, 9}] == {} &]
Select[Flatten[Table[FromDigits/@Tuples[{2,7,9},n],{n,5}]],PrimeQ] (* Harvey P. Dale, Dec 17 2024 *)

from gmpy2 import is_prime
from itertools import product
A261182_list = [int(''.join(d)) for l in range(1,10) for d in product('279',repeat=l) if is_prime(int(''.join(d)))] # Chai Wah Wu, Aug 11 2015

A385779 Primes having only {1, 5, 6} as digits.

Original entry on oeis.org

5, 11, 61, 151, 661, 1151, 1511, 5651, 6151, 6551, 6661, 11161, 11551, 15161, 15511, 15551, 15661, 16111, 16561, 16651, 16661, 51151, 51511, 51551, 55511, 55661, 56611, 61151, 61511, 61561, 61651, 65111, 65551, 65651, 66161, 111611, 115151, 115561, 151561

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020453, A020454.

Cf. A000040, A385776.

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

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

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

print(list(islice(primes_with("156"), 41))) # uses function/imports in A385776

A107715 Primes having only {0,1,2,3} as digits.

Original entry on oeis.org

2, 3, 11, 13, 23, 31, 101, 103, 113, 131, 211, 223, 233, 311, 313, 331, 1013, 1021, 1031, 1033, 1103, 1123, 1201, 1213, 1223, 1231, 1301, 1303, 1321, 2003, 2011, 2111, 2113, 2131, 2203, 2213, 2221, 2311, 2333, 3001, 3011, 3023, 3121, 3203, 3221, 3301, 3313

Offset: 1

Rick L. Shepherd, May 22 2005

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

Subsequence of A036956.
Cf. A036953 (primes containing digits from set {0, 1, 2}).
Cf. A010051, A007090, A193890, A385776.

a107715 n = a107715_list !! (n-1)
a107715_list = filter ((== 1) . a010051) a007090_list
-- Reinhard Zumkeller, Aug 11 2011

Select[Prime[Range[500]],Max[IntegerDigits[#]]<4&] (* Harvey P. Dale, May 09 2012 *)
Select[FromDigits/@Tuples[{0,1,2,3},4],PrimeQ] (* Harvey P. Dale, Mar 06 2016 *)

from gmpy2 import digits
from sympy import isprime
[int(digits(n,4)) for n in range(1000) if isprime(int(digits(n,4)))] # Chai Wah Wu, Jul 31 2014

print(list(islice(primes_with("0123"), 41))) # uses function/imports in A385776. Jason Bard, Jul 18 2025

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

A363023 Primes having only {1, 6, 9} as digits.

Original entry on oeis.org

11, 19, 61, 191, 199, 619, 661, 691, 911, 919, 991, 1619, 1669, 1699, 1999, 6199, 6619, 6661, 6691, 6911, 6961, 6991, 9161, 9199, 9619, 9661, 11119, 11161, 11699, 11969, 16111, 16619, 16661, 16691, 16699, 19661, 19699, 19919, 19961, 19991, 61169, 61961

Offset: 1

Harvey P. Dale, May 13 2023

Jason Bard, Table of n, a(n) for n = 1..10000 (first 2500 terms from Harvey P. Dale)
Index to entries for primes with digits in a given set

Cf. A020454 (1 and 6), A020457 (1 and 9).

Cf. A385776.

Table[Select[Flatten[10#+{1,9}&/@FromDigits/@Tuples[{1,6,9},n]],PrimeQ],{n,4}]//Flatten

A385770 Primes having only {0, 6, 7} as digits.

Original entry on oeis.org

7, 67, 607, 677, 6007, 6067, 6607, 7607, 60077, 60607, 66067, 67607, 67777, 70067, 70607, 70667, 76607, 76667, 76777, 606077, 606607, 607007, 607067, 607667, 660067, 660607, 666067, 666607, 666667, 666707, 670777, 676007, 677077, 677767, 700067

Offset: 1

Jason Bard, Jul 09 2025

			6007 is a term because it is prime and has only {0,6,7} as digits.

Subsequence of A030432.

Cf. A000040, A020469, A385776.

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

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

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

print(list(islice(primes_with("067"), 41))) # uses function/imports in A385776

A385773 Primes having only {1, 2, 5} as digits.

Original entry on oeis.org

2, 5, 11, 151, 211, 251, 521, 1151, 1511, 2111, 2221, 2251, 2521, 2551, 5521, 11251, 11551, 12211, 12251, 12511, 15121, 15511, 15551, 21121, 21211, 21221, 21521, 22111, 22511, 25111, 25121, 51151, 51511, 51521, 51551, 52121, 52511, 55511, 111121, 111211

Offset: 1

Jason Bard, Jul 09 2025

Supersequence of A024050, A020453.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 2, 5]];

Flatten[Table[ Select[FromDigits /@ Tuples[{1, 2, 5}, n], PrimeQ], {n, 7}]]

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

print(list(islice(primes_with("125"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A385768 Primes having only {0, 4, 9} as digits.

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A385800 Primes having only {6, 8, 9} as digits.

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A214704 Primes that contain only the digits (2, 3, 7).

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Magma

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A261182 Primes having only {2, 7, 9} as digits.

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Magma

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A385779 Primes having only {1, 5, 6} as digits.

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A107715 Primes having only {0,1,2,3} as digits.

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

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Magma

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A363023 Primes having only {1, 6, 9} as digits.

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