A199325 -id:A199325 - cp's OEIS frontend

A199303 Palindromic primes in the sense of A007500 with digits '0', '1' and '3' only.

3, 11, 13, 31, 101, 113, 131, 311, 313, 1031, 1033, 1103, 1301, 3011, 3301, 10301, 10333, 11003, 11311, 13331, 30011, 30103, 31013, 31033, 33013, 33301, 101333, 110311, 113011, 113131, 131311, 133033, 133103, 301331, 301333, 330331, 333101, 333103, 1000033, 1001003, 1001303, 1003001

Offset: 1

M. F. Hasler, Nov 04 2011

Chai Wah Wu, Table of n, a(n) for n = 1..6114

Cf. A020449 - A020472, A199325 - A199329, A199302 - A199306.

[p: p in PrimesUpTo(10^8) | Set(Intseq(p)) subset [0, 1, 3] and IsPrime(Seqint(Reverse(Intseq(p))))]; // Bruno Berselli, Nov 07 2011

Flatten[{#,IntegerReverse[#]}&/@Select[FromDigits/@Tuples[{0,1,3},7],AllTrue[ {#,IntegerReverse[ #]},PrimeQ]&]]//Union (* Harvey P. Dale, Sep 12 2023 *)

allow=Vec("013"); forprime(p=1, default(primelimit), setminus( Set( Vec( Str( p ))), allow)&next; isprime(A004086(p))&print1(p", ")) /* for illustrative purpose only: better use the code below */

a(n=50,list=0,L=[0,1,3],needpal=1)={ 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; needpal & !isprime(A004086(t)) & next; list & print1(t","); n-- || return(t)))}  \\ M. F. Hasler, Nov 06 2011

from itertools import product
from sympy import isprime
A199303_list = [n for n in (int(''.join(s)) for s in product('013',repeat=12)) if isprime(n) and isprime(int(str(n)[::-1]))] # Chai Wah Wu, Dec 17 2015

A199328 Palindromic primes in the sense of A007500 with digits '0', '1' and '8' only.

Original entry on oeis.org

11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 180181, 180811, 181081, 188011, 188801, 1008001, 1088081, 1110881, 1180811, 1181881, 1808801, 1880111, 1880881, 1881811, 1881881, 10001081, 10001801, 10011101, 10080011, 10101181, 10111001, 10111081, 10180801, 10188811, 10808101, 10810001

Offset: 1

M. F. Hasler, Nov 05 2011

Harvey P. Dale, Table of n, a(n) for n = 1..10000 (First 4188 terms from Chai Wah Wu.)

Intersection of A007500 and A061247.

Cf. A020449-A020472, A199325-A199329.

Select[10#+1&/@FromDigits/@Tuples[{0,1,8},7],AllTrue[{#,IntegerReverse[#]},PrimeQ]&] (* Harvey P. Dale, Mar 28 2025 *)

a(n=50,L=[0,1,8],show=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;isprime(A004086(t))||next;show&print1(t",");n--||return(t)))}

from itertools import product
from sympy import isprime
A199328_list = [n for n in (int(''.join(s)) for s in product('018',repeat=10)) if isprime(n) and isprime(int(str(n)[::-1]))] # Chai Wah Wu, Dec 17 2015

A199304 Palindromic primes in the sense of A007500 with digits '0', '1' and '4' only.

Original entry on oeis.org

11, 101, 11411, 100411, 101141, 114001, 114041, 140411, 141101, 1004141, 1010411, 1040141, 1041041, 1100441, 1114111, 1140101, 1144441, 1401401, 1410401, 1411141, 1414001, 1440011, 1444411, 1444441, 10010411, 10011101, 10041011, 10044011

Offset: 1

M. F. Hasler, Nov 04 2011

All terms start and end with the digit 1.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A020449 - A020472, A199325 - A199329, A199302 - A199306.

[p: p in PrimesUpTo(10^8) | Set(Intseq(p)) subset [0,1,4] and IsPrime(Seqint(Reverse(Intseq(p))))];  // Bruno Berselli, Nov 07 2011

F:= proc(d) local A0, A4, Res, q, r;
   Res:= NULL;
   q:= (10^(d+1)-1)/9;
   for A0 in combinat:-powerset({$1..d-1}) do
     for A4 in combinat:-powerset({$1..d-1} minus A0) do
       r:= q - add(10^i,i=A0) + 3*add(10^i,i=A4);
       if isprime(r) and isprime(q - add(10^(d-i),i=A0) + 3*add(10^(d-i),i=A4)) then
          Res:= Res, r
       fi
   od od;
   Res
end proc:
sort([seq(F(d),d=1..7)]); # Robert Israel, May 03 2018

allow=Vec("014");forprime(p=1,default(primelimit),setminus( Set( Vec(Str( p ))),allow)&next;isprime(A004086(p))&print1(p",")) /* better use the more efficient code below */

a(n=50,list=0,L=[0,1,4],needpal=1)={ 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; needpal & !isprime(A004086(t)) & next; list & print1(t","); n-- || return(t)))}  \\ M. F. Hasler, Nov 06 2011

A386018 Primes having only {0, 1, 2, 5} as digits.

Original entry on oeis.org

2, 5, 11, 101, 151, 211, 251, 521, 1021, 1051, 1151, 1201, 1511, 2011, 2111, 2221, 2251, 2521, 2551, 5011, 5021, 5051, 5101, 5501, 5521, 10111, 10151, 10211, 10501, 11251, 11551, 12011, 12101, 12211, 12251, 12511, 15101, 15121, 15511, 15551, 20011, 20021, 20051

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A036953, A199325, A385773.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 5]];

Select[FromDigits /@ Tuples[{0, 1, 2, 5}, n], PrimeQ]

primes_with(, 1, [0, 1, 2, 5]) \\ uses function in A385776

print(list(islice(primes_with("0125"), 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

A386027 Primes having only {0, 1, 4, 5} as digits.

Original entry on oeis.org

5, 11, 41, 101, 151, 401, 541, 1051, 1151, 1451, 1511, 4001, 4051, 4111, 4441, 4451, 5011, 5051, 5101, 5441, 5501, 10111, 10141, 10151, 10501, 11411, 11551, 14011, 14051, 14401, 14411, 14551, 15101, 15401, 15451, 15511, 15541, 15551, 40111, 40151, 41011, 41051

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A199325, A260266, A260268.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 4, 5]];

Select[FromDigits /@ Tuples[{0, 1, 4, 5}, n], PrimeQ]

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

print(list(islice(primes_with("0145"), 41))) # uses function/imports in A385776

A386031 Primes having only {0, 1, 5, 6} as digits.

Original entry on oeis.org

5, 11, 61, 101, 151, 601, 661, 1051, 1061, 1151, 1511, 1601, 5011, 5051, 5101, 5501, 5651, 6011, 6101, 6151, 6551, 6661, 10061, 10111, 10151, 10501, 10601, 10651, 11161, 11551, 15061, 15101, 15161, 15511, 15551, 15601, 15661, 16001, 16061, 16111, 16561, 16651

Offset: 1

Jason Bard, Jul 14 2025

Primes with decimal digits only in the set {0,1} mod 5.

Supersequence of A199325, A199326, A385779.

Cf. A000040, A030430, A385776.

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

Select[FromDigits/@Tuples[{0,1,5,6},5],PrimeQ]

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

print(list(islice(primes_with("0156"), 41))) # uses function/imports in A385776

Mathematica program corrected by Harvey P. Dale, Aug 27 2025

A386032 Primes having only {0, 1, 5, 7} as digits.

Original entry on oeis.org

5, 7, 11, 17, 71, 101, 107, 151, 157, 557, 571, 577, 701, 751, 757, 1051, 1117, 1151, 1171, 1511, 1571, 1777, 5011, 5051, 5077, 5101, 5107, 5171, 5501, 5507, 5557, 5701, 5711, 5717, 7001, 7057, 7151, 7177, 7507, 7517, 7577, 7717, 7757, 10007, 10111, 10151, 10177

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A199325, A199327, A260828.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 5, 7]];

Select[FromDigits /@ Tuples[{0, 1, 5, 7}, n], PrimeQ]

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

print(list(islice(primes_with("0157"), 41))) # uses function/imports in A385776

A386033 Primes having only {0, 1, 5, 8} as digits.

Original entry on oeis.org

5, 11, 101, 151, 181, 811, 881, 1051, 1151, 1181, 1511, 1801, 1811, 5011, 5051, 5081, 5101, 5501, 5581, 5801, 5851, 5881, 8011, 8081, 8101, 8111, 8501, 8581, 10111, 10151, 10181, 10501, 11551, 11801, 15101, 15511, 15551, 15581, 15881, 18181, 50051, 50101, 50111

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A061247, A199325, A385780.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 5, 8]];

Select[FromDigits /@ Tuples[{0, 1, 5, 8}, n], PrimeQ]

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

print(list(islice(primes_with("0158"), 41))) # uses function/imports in A385776

A386034 Primes having only {0, 1, 5, 9} as digits.

Original entry on oeis.org

5, 11, 19, 59, 101, 109, 151, 191, 199, 509, 599, 911, 919, 991, 1009, 1019, 1051, 1091, 1109, 1151, 1511, 1559, 1901, 1951, 1999, 5009, 5011, 5051, 5059, 5099, 5101, 5119, 5501, 5519, 5591, 9001, 9011, 9059, 9091, 9109, 9151, 9199, 9511, 9551, 9901, 10009, 10091

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A199325, A199329, A385781.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 5, 9]];

Select[FromDigits /@ Tuples[{0, 1, 5, 9}, n], PrimeQ]

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

print(list(islice(primes_with("0159"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A199303 Palindromic primes in the sense of A007500 with digits '0', '1' and '3' only.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

Python

A199328 Palindromic primes in the sense of A007500 with digits '0', '1' and '8' only.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

A199304 Palindromic primes in the sense of A007500 with digits '0', '1' and '4' only.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

PARI

PARI

A386018 Primes having only {0, 1, 2, 5} as digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A386027 Primes having only {0, 1, 4, 5} as digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A386031 Primes having only {0, 1, 5, 6} as digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python