A199329 -id:A199329 - cp's OEIS frontend

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

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

A306855 Primes of the form 10^i + 10^j - 1.

Original entry on oeis.org

19, 109, 199, 1009, 1999, 10009, 10099, 100999, 199999, 1000099, 1000999, 19999999, 1000000009, 1000009999, 1000099999, 1009999999, 10000000999, 10000099999, 10999999999, 100999999999, 1000000009999, 1000000999999, 1099999999999, 10000000000099, 10009999999999, 100000000000099, 100000009999999

Offset: 1

Robert Israel, Mar 13 2019

Primes p such that p+1 is in A052216.

Primes of the following form in base 10: 1, followed by 0 or more 0's, then 1 or more 9's.

Robert Israel, Table of n, a(n) for n = 1..2000

Cf. A052216. Subsequence of A199329.

select(isprime, [seq(seq(10^n+10^m-1, m=1..n),n=1..15)]);

Select[Flatten[Table[FromDigits[Join[PadRight[{1},n,0],PadRight[{},m,9]]],{n,20},{m,20}]],PrimeQ]//Sort (* Harvey P. Dale, May 15 2021 *)

A386022 Primes having only {0, 1, 2, 9} as digits.

Original entry on oeis.org

2, 11, 19, 29, 101, 109, 191, 199, 211, 229, 911, 919, 929, 991, 1009, 1019, 1021, 1091, 1109, 1129, 1201, 1229, 1291, 1901, 1999, 2011, 2029, 2099, 2111, 2129, 2221, 2909, 2999, 9001, 9011, 9029, 9091, 9109, 9199, 9209, 9221, 9901, 9929, 10009, 10091, 10099

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A036953, A199329, A385776.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 9]];

Select[FromDigits /@ Tuples[{0, 1, 2, 9}, n], PrimeQ]

primes_with(, 1, [0, 1, 2, 9]) \\ uses function in A385776

print(list(islice(primes_with("0129"), 41))) # uses function/imports in A385776

A386026 Primes having only {0, 1, 3, 9} as digits.

Original entry on oeis.org

3, 11, 13, 19, 31, 101, 103, 109, 113, 131, 139, 191, 193, 199, 311, 313, 331, 911, 919, 991, 1009, 1013, 1019, 1031, 1033, 1039, 1091, 1093, 1103, 1109, 1193, 1301, 1303, 1319, 1399, 1901, 1913, 1931, 1933, 1993, 1999, 3001, 3011, 3019, 3109, 3119, 3191, 3301

Offset: 1

Jason Bard, Jul 14 2025

Primes that only contain digits that are 0 or integer powers of 3.

Supersequence of A199329, A260044, A329761.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 3, 9]];

Select[FromDigits /@ Tuples[{0, 1, 3, 9}, n], PrimeQ]

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

print(list(islice(primes_with("0139"), 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

A386037 Primes having only {0, 1, 6, 9} as digits.

Original entry on oeis.org

11, 19, 61, 101, 109, 191, 199, 601, 619, 661, 691, 911, 919, 991, 1009, 1019, 1061, 1069, 1091, 1109, 1601, 1609, 1619, 1669, 1699, 1901, 1999, 6011, 6091, 6101, 6199, 6619, 6661, 6691, 6911, 6961, 6991, 9001, 9011, 9091, 9109, 9161, 9199, 9601, 9619, 9661, 9901

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A199326, A199329, A363023.

Cf. A000040, A385776.

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

f:= n-> (l-> add([0, 1, 6, 9][l[j]+1]*10^(j-1), j=1..nops(l)))(convert(n, base, 4)):
select(isprime, [seq(f(i), i=0..250)])[];  # Alois P. Heinz, Jul 15 2025

Select[FromDigits /@ Tuples[{0, 1, 6, 9}, n], PrimeQ]

primes_with(, 1, [0, 1, 6, 9]) \\ uses function in A385776

print(list(islice(primes_with("0169"), 41))) # uses function/imports in A385776

A386039 Primes having only {0, 1, 7, 9} as digits.

Original entry on oeis.org

7, 11, 17, 19, 71, 79, 97, 101, 107, 109, 179, 191, 197, 199, 701, 709, 719, 797, 907, 911, 919, 971, 977, 991, 997, 1009, 1019, 1091, 1097, 1109, 1117, 1171, 1709, 1777, 1901, 1907, 1979, 1997, 1999, 7001, 7019, 7079, 7109, 7177, 7717, 7901, 7907, 7919, 9001

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A199327, A199329, A260893.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 7, 9]];

Select[FromDigits /@ Tuples[{0, 1, 7, 9}, n], PrimeQ]

primes_with(, 1, [0, 1, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("0179"), 41))) # uses function/imports in A385776

A386040 Primes having only {0, 1, 8, 9} as digits.

Original entry on oeis.org

11, 19, 89, 101, 109, 181, 191, 199, 809, 811, 881, 911, 919, 991, 1009, 1019, 1091, 1109, 1181, 1801, 1811, 1889, 1901, 1999, 8009, 8011, 8081, 8089, 8101, 8111, 8191, 8819, 8999, 9001, 9011, 9091, 9109, 9181, 9199, 9811, 9901, 10009, 10091, 10099, 10111, 10181

Offset: 1

Jason Bard, Jul 15 2025

Supersequence of A061247, A199329, A385783.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 8, 9]];

Select[FromDigits /@ Tuples[{0, 1, 8, 9}, n], PrimeQ]

primes_with(, 1, [0, 1, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("0189"), 41))) # uses function/imports in A385776

A199305 Palindromic primes in the sense of A007500 with digits '0', '1' and '5' only.

Original entry on oeis.org

5, 11, 101, 151, 1151, 1511, 10151, 10501, 11551, 15101, 15511, 15551, 100511, 110051, 115001, 150011, 150151, 151051, 1001551, 1051051, 1055501, 1115551, 1150151, 1150511, 1501501, 1510511, 1550551, 1551001, 1551551, 1555111, 10000511, 10011101, 10011511, 10055011, 10101551

Offset: 1

M. F. Hasler, Nov 06 2011

All terms, except for the initial 5, start and end with the digit '1'. This fact could be used to significantly speed up the given program.

Cf. A020449-A020472, A199325-A199329, A087510-A087515.

[p: p in PrimesUpTo(10^8) | Set(Intseq(p)) subset [0,1,5] and IsPrime(Seqint(Reverse(Intseq(p))))]; // Bruno Berselli, Nov 07 2011

a(n=50, list=0, L=[0, 1, 5], 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

cp's OEIS Frontend

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

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

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Magma

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PARI

A306855 Primes of the form 10^i + 10^j - 1.

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Maple

Mathematica

A386022 Primes having only {0, 1, 2, 9} as digits.

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Magma

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A386026 Primes having only {0, 1, 3, 9} as digits.

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Magma

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

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Magma

Mathematica

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A386037 Primes having only {0, 1, 6, 9} as digits.

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Magma

Maple

Mathematica

PARI

Python

A386039 Primes having only {0, 1, 7, 9} as digits.