A199340 -id:A199340 - cp's OEIS frontend

A199346 Primes having only {3, 4, 6} as digits.

3, 43, 433, 443, 463, 643, 3343, 3433, 3463, 3643, 4363, 4463, 4643, 4663, 6343, 33343, 36343, 36433, 36643, 43633, 44633, 46633, 46643, 46663, 63443, 63463, 64333, 64433, 64633, 64663, 66343, 66463, 66643, 333433, 334333, 334363, 334643, 336463, 336643, 343333, 343433, 344363, 346433, 363343, 363463, 364333, 364433, 364643

Offset: 1

M. F. Hasler, Nov 05 2011

All terms end in 3 and have a number of digits '4' that is not divisible by 3.

A020461 is a subsequence. - Vincenzo Librandi, Jul 29 2015

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A020449 - A020472, A199325 - A199329, A385768 - A385800.

Cf. similar sequences listed in A199340.

[p: p in PrimesUpTo(4*10^5) | Set(Intseq(p)) subset [3, 4, 6]]; // Vincenzo Librandi, Jul 29 2015

Select[Flatten[Table[FromDigits/@(Flatten[{#,3},1]&/@Tuples[{3,4,6},n]),{n,0,5}]],PrimeQ] (* Harvey P. Dale, Jan 01 2013 *)
Select[Prime[Range[10^5]], Complement[IntegerDigits[#], {3, 4, 6}]=={}&] (* Vincenzo Librandi, Jul 28 2015 *)

a(n, list=0, L=[3, 4, 6], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u) || next; reqpal & !isprime(A004086(t)) & next; list & print1(t", "); n--||return(t)))}

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 *)

A111488 Primes having only {0, 1, 3, 6} as digits.

Original entry on oeis.org

3, 11, 13, 31, 61, 101, 103, 113, 131, 163, 311, 313, 331, 601, 613, 631, 661, 1013, 1031, 1033, 1061, 1063, 1103, 1163, 1301, 1303, 1361, 1601, 1613, 1663, 3001, 3011, 3061, 3163, 3301, 3313, 3331, 3361, 3613, 3631, 6011, 6101, 6113, 6131, 6133, 6163

Offset: 1

Jonathan Vos Post, Nov 15 2005

Includes all repunit primes (A004022). Conjecture: an infinite sequence. Note twin primes: (11, 13), (101, 103), (311, 313), (1031, 1033), (1061, 1063), (1301, 1303), (6131, 6133), (10301, 10303), (10331, 10333), (13001, 13003).
In other words, primes with digits in the set {0,1,3,6}. - M. F. Hasler, Jul 25 2015
The number of 1's in the representation must be either 1 or 2 (mod 3), because otherwise the number would be divisible by 3 (and therefore composite). The only exception is the 3 itself. This excludes basically members of A038603. - R. J. Mathar, Jul 25 2015

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

Cf. A000040, A000217, A004022, A038603.

Cf. also A020450 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

f:= proc(x) local L,p;
  L:= subs([3=6,2=3],convert(x,base,4));
  p:= add(L[i]*10^(i-1),i=1..nops(L));
  if isprime(p) then p fi
end proc:
map(f, [$1..4^4]); # Robert Israel, Dec 18 2018

Select[Prime@ Range@ 1000, SubsetQ[{0, 1, 3, 6}, IntegerDigits@ #] &] (* Michael De Vlieger, Jul 25 2015 *)

A111488={(n, show=0, L=[0,1,3,6])->my(t); for(d=1,1e9,u=vector(d, i, 10^(d-i))~; forvec(v=vector(d,i,[1+(i==1&&!L[1]), #L]), ispseudoprime(t=vector(d, i, L[v[i]])*u)||next; show&print1(t", "); n--||return(t)))} \\ M. F. Hasler, Jul 25 2015

Corrected by Ray Chandler, Nov 19 2005

Name changed by Sean A. Irvine, Jul 21 2025

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

A386057 Primes having only {0, 3, 4, 6} as digits.

Original entry on oeis.org

3, 43, 433, 443, 463, 643, 3343, 3433, 3463, 3643, 4003, 4363, 4463, 4603, 4643, 4663, 6043, 6343, 30403, 30643, 33343, 33403, 34033, 34303, 34403, 34603, 36343, 36433, 36643, 40063, 40343, 40433, 43003, 43063, 43403, 43633, 44633, 46633, 46643, 46663, 60343

Offset: 1

Jason Bard, Jul 15 2025

Subsequence of A030431.
Supersequence of A199340, A199346.
Cf. A000040, A385776.

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

Select[FromDigits /@ Tuples[{0, 3, 4, 6}, n], PrimeQ]

primes_with(, 1, [0, 3, 4, 6]) \\ uses function in A385776

print(list(islice(primes_with("0346"), 41))) # uses function/imports in A385776

A386058 Primes having only {0, 3, 4, 7} as digits.

Original entry on oeis.org

3, 7, 37, 43, 47, 73, 307, 337, 347, 373, 433, 443, 733, 743, 773, 3037, 3307, 3343, 3347, 3373, 3407, 3433, 3733, 4003, 4007, 4073, 4337, 4373, 4447, 4703, 4733, 7043, 7307, 7333, 7433, 7477, 7703, 30047, 30307, 30347, 30403, 30703, 30707, 30773, 33037, 33073

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A199340, A199347, A260378, A384449.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 4, 7]];

Select[FromDigits /@ Tuples[{0, 3, 4, 7}, n], PrimeQ]

primes_with(, 1, [0, 3, 4, 7]) \\ uses function in A385776

print(list(islice(primes_with("0347"), 41))) # uses function/imports in A385776

A386059 Primes having only {0, 3, 4, 8} as digits.

Original entry on oeis.org

3, 43, 83, 383, 433, 443, 883, 3083, 3343, 3433, 3803, 3833, 4003, 4483, 8443, 8803, 30403, 30803, 33083, 33343, 33403, 34033, 34303, 34403, 34483, 34843, 34883, 38083, 38303, 38333, 38803, 38833, 40343, 40433, 40483, 40883, 43003, 43403, 44383, 44483, 44843

Offset: 1

Jason Bard, Jul 15 2025

Subsequence of A030431.
Supersequence of A199340, A199348, A261434.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 4, 8]];

Select[FromDigits /@ Tuples[{0, 3, 4, 8}, n], PrimeQ]

primes_with(, 1, [0, 3, 4, 8]) \\ uses function in A385776

print(list(islice(primes_with("0348"), 41))) # uses function/imports in A385776

A386060 Primes having only {0, 3, 4, 9} as digits.

Original entry on oeis.org

3, 43, 349, 409, 433, 439, 443, 449, 499, 3049, 3343, 3433, 3449, 3499, 3943, 4003, 4049, 4093, 4099, 4339, 4349, 4409, 4493, 4903, 4909, 4933, 4943, 4993, 4999, 9043, 9049, 9343, 9349, 9403, 9433, 9439, 9949, 30403, 30449, 30493, 30949, 33049, 33343, 33349, 33403

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A199340, A199349, A385768.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 3, 4, 9]];

Select[FromDigits /@ Tuples[{0, 3, 4, 9}, n], PrimeQ]

primes_with(, 1, [0, 3, 4, 9]) \\ uses function in A385776

print(list(islice(primes_with("0349"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A199346 Primes having only {3, 4, 6} as digits.

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

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A111488 Primes having only {0, 1, 3, 6} as digits.

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

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A386057 Primes having only {0, 3, 4, 6} as digits.

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A386058 Primes having only {0, 3, 4, 7} as digits.

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A386059 Primes having only {0, 3, 4, 8} as digits.

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Magma

Mathematica

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Python

A386060 Primes having only {0, 3, 4, 9} as digits.