A260044 -id:A260044 - cp's OEIS frontend

A199329 Primes having only {0, 1, 9} as digits.

11, 19, 101, 109, 191, 199, 911, 919, 991, 1009, 1019, 1091, 1109, 1901, 1999, 9001, 9011, 9091, 9109, 9199, 9901, 10009, 10091, 10099, 10111, 10909, 11119, 11909, 19001, 19009, 19919, 19991, 90001, 90011, 90019, 90191, 90199, 90901, 90911, 91009, 91019, 91099, 91199, 91909, 99109, 99119, 99191, 99901, 99991

Offset: 1

M. F. Hasler, Nov 05 2011

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

Cf. A020449 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199327, A061247, A199340 - A199349.

Select[FromDigits/@Tuples[{0,1,9},5],PrimeQ] (* Harvey P. Dale, Dec 10 2016 *)

A199329(n=50,show=0,L=[0,1,9])={for(d=1,1e9,my(t,u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,[1+!(L[1]||(i>1&&iM. F. Hasler, Jul 25 2015

A036953 Primes having only {0, 1, 2} as digits.

Original entry on oeis.org

2, 11, 101, 211, 1021, 1201, 2011, 2111, 2221, 10111, 10211, 12011, 12101, 12211, 20011, 20021, 20101, 20201, 21001, 21011, 21101, 21121, 21211, 21221, 22111, 101021, 101111, 101221, 102001, 102101, 102121, 110221, 111121, 111211, 112111

Offset: 1

Patrick De Geest, Jan 04 1999

Number of n-digit terms d(n) = (1, 1, 2, 5, 16, 34, 76, 194, 543, 1469, 4094, 11017, ...); e.g., there are five 4-digit terms: 1021, 1201, 2011, 2111, 2221, hence d(4) = 5. - Zak Seidov, Jun 30 2013

Also, primes in A007089. - M. F. Hasler, Jul 25 2015

Zak Seidov, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
Index to entries for primes with digits in a given set

Subsequence of A107715.
Cf. A036952-A036964.
Cf. A020450 - A020472, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349, A217039, A079651.

Select[FromDigits/@Tuples[{0,1,2},6],PrimeQ] (* Harvey P. Dale, Jul 11 2017 *)

lista(n) = {forprime(p=2, n, if (vecmax(digits(p)) <= 2, print1(p, ", ")))} \\ Michel Marcus, Aug 02 2014

A036953={(n,show=0)->for(d=1,1e9,my(u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,if(i>1,if(iM. F. Hasler, Jul 25 2015

from gmpy2 import digits
from sympy import isprime
[int(digits(n,3)) for n in range(1000) if isprime(int(digits(n,3)))] # Chai Wah Wu, Jul 31 2014

Edited by M. F. Hasler, Jul 25 2015

A260266 Primes having only {0, 1, 4} as digits.

Original entry on oeis.org

11, 41, 101, 401, 4001, 4111, 4441, 10111, 10141, 11411, 14011, 14401, 14411, 40111, 41011, 41141, 41411, 44041, 44101, 44111, 100411, 101111, 101141, 101411, 110441, 114001, 114041, 140111, 140401, 140411, 141041, 141101, 400441, 401101, 401411, 404011

Offset: 1

Vincenzo Librandi, Jul 22 2015

A020449 and A020452 are subsequences.

All terms end with a digit "1". - M. F. Hasler, Jul 26 2015

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

Primes that contain only digits among {1,4,k}: this sequence (k=0), A260267 (k=2), A199341 (k=3), A260268 (k=5), A260269 (k=6), A079651 (k=7), A260270 (k=8), A260271 (k=9).
Cf. A020449, A020452.
Cf. A020450 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

[p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [1, 4, 0]];

Select[Prime[Range[4 10^4]], Complement[IntegerDigits[#], {1, 4, 0}]=={} &]

A260266(n=50,show=0)={for(d=1,1e9,my(t,u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,[i==1||i==d,1+(iM. F. Hasler, Jul 25 2015

A199327 Primes having only {0, 1, 7} as digits.

Original entry on oeis.org

7, 11, 17, 71, 101, 107, 701, 1117, 1171, 1777, 7001, 7177, 7717, 10007, 10111, 10177, 10711, 10771, 11071, 11117, 11171, 11177, 11701, 11717, 11777, 17011, 17077, 17107, 17117, 17707, 70001, 70111, 70117, 70177, 70717, 71011, 71171, 71707, 71711, 71777, 77017, 77101, 77171, 77711, 101107, 101111, 101117

Offset: 1

M. F. Hasler, Nov 05 2011

Harvey P. Dale, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).

Cf. A020449 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

[p: p in PrimesUpTo(80000) | Intseq(p) subset {0,1,7}]; // Vincenzo Librandi, Jan 16 2020

f[i_,nn_]:=Select[Flatten[Table[FromDigits/@(Join[{i},#]&/@Tuples[ {0,1,7}, n]), {n,0,nn}]],PrimeQ]; Union[Join[f[1,6],f[7,6]]] (* Harvey P. Dale, Nov 19 2011 *)
Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {0, 1, 7}]=={}&] (* Vincenzo Librandi, Jan 16 2020 *)

a(n,list=0,L=[0,1,7])={for(d=1,1e9,my(t,u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,[1+!(L[1]||(i>1&&iM. F. Hasler, Jul 26 2015

A217039 Primes having only {4, 5, 7} as digits.

Original entry on oeis.org

5, 7, 47, 457, 547, 557, 577, 757, 4447, 4457, 4547, 5477, 5557, 7457, 7477, 7547, 7577, 7757, 44777, 45557, 45757, 47777, 54547, 54577, 55457, 55547, 57457, 57557, 74747, 75557, 75577, 77447, 77477, 77557, 77747, 444547, 444557, 445447, 445477, 445747, 447757

Offset: 1

Jonathan Vos Post, Sep 24 2012

These are the primes in A214584. Primes whose numerals are all written (san serif) with at least one right or acute angle.

Cf. A079651, A079652, A214584.

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

[p: p in PrimesUpTo(450000) | Intseq(p) subset [4,5,7]]; // Bruno Berselli, Sep 25 2012

Select[Flatten[Table[FromDigits/@Tuples[{4,5,7},n],{n,6}]],PrimeQ] (* Bruno Berselli, Sep 25 2012 *)

A217039(n=50,show=0,L=[4,5,7])={for(d=1,1e9, my(t, u=vector(d,i,10^(d-i))~); forvec(v=vector(d,i,[if(i==d&&d>1,3/*must end in 7*/,1), #L]), ispseudoprime(t=vecextract(L, v)*u)||next; show&&print1(t", "); n--||return(t)))} \\ Syntax updated for newer PARI versions by M. F. Hasler, Jul 25 2015

A000040 INTERSECTION A214584.

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

A386023 Primes having only {0, 1, 3, 4} as digits.

Original entry on oeis.org

3, 11, 13, 31, 41, 43, 101, 103, 113, 131, 311, 313, 331, 401, 431, 433, 443, 1013, 1031, 1033, 1103, 1301, 1303, 1433, 3001, 3011, 3041, 3301, 3313, 3331, 3343, 3413, 3433, 4001, 4003, 4013, 4111, 4133, 4441, 10103, 10111, 10133, 10141, 10301, 10303, 10313, 10331

Offset: 1

Jason Bard, Jul 14 2025

Subsequence of A036956.
Supersequence of A199341, A260044, A260266.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 3, 4]];

Select[FromDigits /@ Tuples[{0, 1, 3, 4}, n], PrimeQ]

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

print(list(islice(primes_with("0134"), 41))) # uses function/imports in A385776

A386024 Primes having only {0, 1, 3, 5} as digits.

Original entry on oeis.org

3, 5, 11, 13, 31, 53, 101, 103, 113, 131, 151, 311, 313, 331, 353, 503, 1013, 1031, 1033, 1051, 1103, 1151, 1153, 1301, 1303, 1511, 1531, 1553, 3001, 3011, 3301, 3313, 3331, 3511, 3533, 5003, 5011, 5051, 5101, 5113, 5153, 5303, 5333, 5351, 5501, 5503, 5531, 10103

Offset: 1

Jason Bard, Jul 14 2025

Subsequence of A036958.
Supersequence of  A199325, A260044, A260224.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 3, 5]];

Select[FromDigits /@ Tuples[{0, 1, 3, 5}, n], PrimeQ]

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

print(list(islice(primes_with("0135"), 41))) # uses function/imports in A385776

A386025 Primes having only {0, 1, 3, 7} as digits.

Original entry on oeis.org

3, 7, 11, 13, 17, 31, 37, 71, 73, 101, 103, 107, 113, 131, 137, 173, 307, 311, 313, 317, 331, 337, 373, 701, 733, 773, 1013, 1031, 1033, 1103, 1117, 1171, 1301, 1303, 1307, 1373, 1733, 1777, 3001, 3011, 3037, 3137, 3301, 3307, 3313, 3331, 3371, 3373, 3701, 3733

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A199327, A260044, A260379.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 3, 7]];

Select[FromDigits /@ Tuples[{0, 1, 3, 7}, n], PrimeQ]

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

print(list(islice(primes_with("0137"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A199329 Primes having only {0, 1, 9} as digits.

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A036953 Primes having only {0, 1, 2} as digits.

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A260266 Primes having only {0, 1, 4} as digits.

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Magma

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A199327 Primes having only {0, 1, 7} as digits.

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Magma

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A217039 Primes having only {4, 5, 7} as digits.

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Magma

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

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Magma

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

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A386023 Primes having only {0, 1, 3, 4} as digits.

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