A260223 -id:A260223 - cp's OEIS frontend

A260225 Primes having only {3, 5, 6} as digits.

3, 5, 53, 353, 563, 653, 3533, 5333, 5563, 5653, 6353, 6553, 6563, 6653, 33353, 33533, 33563, 35353, 35363, 35533, 36353, 36563, 36653, 53353, 53633, 53653, 55333, 55633, 55663, 56333, 56533, 56633, 56663, 63353, 63533, 65353, 65563, 65633, 66533, 66553

Offset: 1

Vincenzo Librandi, Jul 21 2015

A020462 is subsequence.

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

Cf. similar sequences listed in A260223.

Cf. A020462.

[p: p in PrimesUpTo(70000) | Set(Intseq(p)) subset [3, 5, 6]];

Select[Prime[Range[3 10^4]], Complement[IntegerDigits[#], {3, 5, 6}]=={} &]
Table[Select[FromDigits/@Tuples[{3,5,6},n],PrimeQ],{n,5}]//Flatten (* Harvey P. Dale, Jan 23 2018 *)

A260226 Primes having only {3, 5, 8} as digits.

Original entry on oeis.org

3, 5, 53, 83, 353, 383, 853, 883, 3533, 3583, 3833, 3853, 5333, 8353, 33353, 33533, 35353, 35533, 38333, 38833, 53353, 55333, 83383, 83833, 85333, 85853, 88853, 88883, 333383, 333533, 335383, 335833, 338383, 353333, 353833, 355853, 383533, 383833, 533353

Offset: 1

Vincenzo Librandi, Jul 22 2015

A020462 and A020464 are subsequences.

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

Cf. similar sequences listed in A260223.

Cf. A020462, A020464.

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [3, 5, 8]];

Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 5, 8}]=={} &]
Select[Flatten[Table[FromDigits/@Tuples[{3,5,8},n],{n,6}]],PrimeQ] (* or  *) Join[{3,5},Select[10#+3&/@Flatten[Table[FromDigits/@Tuples[{3,5,8},n],{n,5}]],PrimeQ]] (* The second program is faster because it recognizes that, except only for 5, each such prime must end in 3. *) (* Harvey P. Dale, Jul 17 2020 *)

A260227 Primes having only {3, 5, 9} as digits.

Original entry on oeis.org

3, 5, 53, 59, 353, 359, 593, 599, 953, 3359, 3533, 3539, 3559, 3593, 5333, 5393, 5399, 5939, 5953, 9533, 9539, 33353, 33359, 33533, 33599, 35339, 35353, 35393, 35533, 35593, 35933, 35993, 35999, 39359, 39953, 53353, 53359, 53593, 53939, 53959, 53993

Offset: 1

Vincenzo Librandi, Jul 22 2015

A020462 and A020468 are subsequences.

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

Cf. similar sequences listed in A260223.

Cf. A020462, A020468.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [3, 5, 9]];

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {3, 5, 9}]=={} &]
Select[Table[FromDigits/@Tuples[{3,5,9},n],{n,5}]//Flatten,PrimeQ] (* Harvey P. Dale, Sep 07 2018 *)

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

A261434 Primes having only {0, 3, 8} as digits.

Original entry on oeis.org

3, 83, 383, 883, 3083, 3803, 3833, 8803, 30803, 33083, 38083, 38303, 38333, 38803, 38833, 80803, 80833, 83003, 83383, 83833, 88003, 88883, 303803, 308003, 308303, 308333, 308383, 330383, 333383, 333803, 338033, 338383, 338803, 380333, 380383, 380803, 383083

Offset: 1

Vincenzo Librandi, Aug 18 2015

A020464 is a subsequence.

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

Cf. Primes that contain only the digits (0,3,k): A260044 (k=1), A260125 (k=2), A199340 (k=4), A260223 (k=5), A260378 (k=7), this sequence (k=8).

Cf. A000040, A020464.

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

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {0, 3, 8}] == {} &]
Select[FromDigits/@Tuples[{0,3,8},6],PrimeQ] (* Harvey P. Dale, Jul 10 2017 *)

A386056 Primes having only {0, 3, 4, 5} as digits.

Original entry on oeis.org

3, 5, 43, 53, 353, 433, 443, 503, 3343, 3433, 3533, 4003, 5003, 5303, 5333, 5443, 5503, 30403, 30553, 33053, 33343, 33353, 33403, 33503, 33533, 34033, 34303, 34403, 34543, 35053, 35353, 35533, 35543, 40343, 40433, 40543, 43003, 43403, 43543, 44053, 44453, 44533

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A199340, A199345, A260223.

Cf. A000040, A030431, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 4, 5]];

f:= n-> (l-> add([0, 3, 4, 5][l[j]+1]*10^(j-1), j=1..nops(l)))(convert(n, base, 4)):
select(isprime, [seq(f(i), i=0..695)])[];  # Alois P. Heinz, Jul 15 2025

Select[FromDigits /@ Tuples[{0, 3, 4, 5}, n], PrimeQ]

primes_with(, 1, [0, 3, 4, 5]) \\ uses function in A385776

print(list(islice(primes_with("0345"), 41))) # uses function/imports in A385776

A386061 Primes having only {0, 3, 5, 6} as digits.

Original entry on oeis.org

3, 5, 53, 353, 503, 563, 653, 3533, 5003, 5303, 5333, 5503, 5563, 5653, 6053, 6353, 6553, 6563, 6653, 30553, 33053, 33353, 33503, 33533, 33563, 35053, 35353, 35363, 35533, 35603, 36353, 36563, 36653, 50033, 50053, 50333, 50363, 50503, 53003, 53353, 53503, 53633

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A260223, A260225.

Cf. A000040, A030431, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 5, 6]];

Select[FromDigits/@Tuples[{0,3,5,6},5],PrimeQ]

primes_with(, 1, [0, 3, 5, 6]) \\ uses function in A385776

print(list(islice(primes_with("0356"), 41))) # uses function/imports in A385776

Mathematica program corrected by Harvey P. Dale, Aug 03 2025

A386062 Primes having only {0, 3, 5, 7} as digits.

Original entry on oeis.org

3, 5, 7, 37, 53, 73, 307, 337, 353, 373, 503, 557, 577, 733, 757, 773, 3037, 3307, 3373, 3533, 3557, 3733, 5003, 5077, 5303, 5333, 5503, 5507, 5557, 5573, 5737, 7057, 7307, 7333, 7507, 7537, 7573, 7577, 7703, 7753, 7757, 30307, 30553, 30557, 30577, 30703, 30707

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A087363, A260223, A260378, A260827.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 5, 7]];

Select[FromDigits /@ Tuples[{0, 3, 5, 7}, n], PrimeQ]

primes_with(, 1, [0, 3, 5, 7]) \\ uses function in A385776

print(list(islice(primes_with("0357"), 41))) # uses function/imports in A385776

A386063 Primes having only {0, 3, 5, 8} as digits.

Original entry on oeis.org

3, 5, 53, 83, 353, 383, 503, 853, 883, 3083, 3533, 3583, 3803, 3833, 3853, 5003, 5303, 5333, 5503, 8053, 8353, 8803, 30553, 30803, 30853, 33053, 33083, 33353, 33503, 33533, 35053, 35083, 35353, 35533, 35803, 38053, 38083, 38303, 38333, 38803, 38833, 50033, 50053

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A260223, A260226, A261434.

Cf. A000040, A030431, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 5, 8]];

Select[FromDigits /@ Tuples[{0, 3, 5, 8}, n], PrimeQ]

primes_with(, 1, [0, 3, 5, 8]) \\ uses function in A385776

print(list(islice(primes_with("0358"), 41))) # uses function/imports in A385776

A386064 Primes having only {0, 3, 5, 9} as digits.

Original entry on oeis.org

3, 5, 53, 59, 353, 359, 503, 509, 593, 599, 953, 3359, 3533, 3539, 3559, 3593, 5003, 5009, 5039, 5059, 5099, 5303, 5309, 5333, 5393, 5399, 5503, 5903, 5939, 5953, 9059, 9533, 9539, 30059, 30509, 30539, 30553, 30559, 30593, 33053, 33353, 33359, 33503, 33533, 33599

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A260223, A260227, A385769.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 5, 9]];

Select[FromDigits /@ Tuples[{0, 3, 5, 9}, n], PrimeQ]

primes_with(, 1, [0, 3, 5, 9]) \\ uses function in A385776

print(list(islice(primes_with("0359"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A260225 Primes having only {3, 5, 6} as digits.

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A260226 Primes having only {3, 5, 8} as digits.

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A260227 Primes having only {3, 5, 9} as digits.

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

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A261434 Primes having only {0, 3, 8} as digits.

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A386056 Primes having only {0, 3, 4, 5} as digits.

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A386061 Primes having only {0, 3, 5, 6} as digits.

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A386062 Primes having only {0, 3, 5, 7} as digits.

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