A385800 -id:A385800 - cp's OEIS frontend

A107666 Primes having only {4, 6, 9} as digits.

449, 499, 4649, 4969, 4999, 6449, 6469, 6949, 9649, 9949, 44449, 44699, 46499, 46649, 49499, 49669, 49999, 64499, 64969, 66449, 66499, 66949, 69499, 94649, 94949, 94999, 96469, 99469, 444449, 444469, 444649, 446969, 449699, 464699, 464999, 466649, 469649, 469969

Offset: 1

Rick L. Shepherd, May 19 2005

Intersection of A000040 and A107665. - K. D. Bajpai, Sep 08 2014

			From _K. D. Bajpai_, Sep 08 2014: (Start)
4649 is a term because it is a prime having only semiprime digits 4, 6 and 9.
6469 is a term because it is a prime having only semiprime digits 4, 6 and 9.
449 is the smallest prime comprising only semiprime digits 4, 6 or 9.
(End)

Jason Bard, Table of n, a(n) for n = 1..10000 (first 2069 terms from K. D. Bajpai)
Index to entries for primes with digits in a given set

Cf. A107665 (numbers with semiprime digits), A001358 (semiprimes), A051416 (primes whose digits are all composite), A020466 (primes with digits 4 and 9 only), A093402 (primes of form 44...9), A093945 (primes of form 499...).
Cf. A107342, A111494, A111496, A111697.
Cf. A385768 - A385800.

N:= 4:  Dgts:= {4, 6, 9}:  A:= NULL:
for d from 1 to N do
K:= combinat[cartprod]([Dgts minus {0}, Dgts $(d-1)]);
while not K[finished] do L:= K[nextvalue]();  x:= add(L[i]*10^(d-i), i=1..d);
if isprime(x) then A:= A, x fi od od: A;  # K. D. Bajpai, Sep 08 2014

Select[Prime[Range[50000]], Intersection[IntegerDigits[#], {0, 1, 2, 3, 5, 7, 8}] == {} &] (* K. D. Bajpai, Sep 08 2014 *)

a(35)-a(38) from K. D. Bajpai, Sep 08 2014

A199342 Primes having only {2, 3, 4} as digits.

Original entry on oeis.org

2, 3, 23, 43, 223, 233, 433, 443, 2243, 2333, 2423, 3323, 3343, 3433, 4243, 4423, 22343, 22433, 23333, 24223, 24443, 32233, 32323, 32423, 32443, 33223, 33343, 42223, 42323, 42433, 42443, 43223, 222323, 223243, 223423, 224233, 224423, 224443, 232333, 232433, 233323, 233423, 234323, 234343, 242243, 243233, 243343, 243433, 244243, 244333

Offset: 1

M. F. Hasler, Nov 05 2011

A020458 and A020461 are subsequences. - Vincenzo Librandi, Jul 28 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(10^6) | Set(Intseq(p)) subset [3, 4, 2]]; // Vincenzo Librandi, Jul 28 2015

Select[Prime[Range[10^5]], Complement[IntegerDigits[#], {3, 4, 2}]=={}&] (* Vincenzo Librandi, Jul 28 2015 *)
Table[Select[FromDigits/@Tuples[{2,3,4},n],PrimeQ],{n,6}]//Flatten (* Harvey P. Dale, Nov 06 2019 *)

a(n, list=0, L=[2, 3, 4], 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)))}

A199345 Primes having only {3, 4, 5} as digits.

Original entry on oeis.org

3, 5, 43, 53, 353, 433, 443, 3343, 3433, 3533, 5333, 5443, 33343, 33353, 33533, 34543, 35353, 35533, 35543, 43543, 44453, 44533, 44543, 45343, 45433, 45533, 45553, 53353, 53453, 54443, 55333, 55343, 333433, 333533, 334333, 335453, 343333, 343433, 343543, 344353, 344453, 344543, 345533, 353333, 353443, 353453, 354353, 354443

Offset: 1

M. F. Hasler, Nov 05 2011

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.

[p: p in PrimesUpTo(4*10^5) | Set(Intseq(p)) subset [3..5]]; // Bruno Berselli, Nov 07 2011

Join[{3,5},Select[Flatten[Table[FromDigits/@(Join[#,{3}]&/@ Tuples[ {3,4,5},n]),{n,5}]],PrimeQ]] (* Harvey P. Dale, Aug 31 2015 *)

a(n, list=0, L=[3, 4, 5], 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)))}

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

Original entry on oeis.org

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)))}

A199348 Primes having only {3, 4, 8} as digits.

Original entry on oeis.org

3, 43, 83, 383, 433, 443, 883, 3343, 3433, 3833, 4483, 8443, 33343, 34483, 34843, 34883, 38333, 38833, 44383, 44483, 44843, 48383, 48883, 83383, 83443, 83833, 83843, 84443, 88843, 88883, 333383, 333433, 334333, 334843, 338383, 343333, 343433, 344483, 344843, 348433, 348443, 348833, 348883, 383483, 383833, 384343, 384383, 388483

Offset: 1

M. F. Hasler, Nov 05 2011

All terms end in 3 and those > 3 never have the same number of 4's and 8's.

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.

Table[Select[FromDigits/@Tuples[{3,4,8},n],PrimeQ],{n,6}]//Flatten (* Harvey P. Dale, Apr 09 2022 *)

a(n, list=0, L=[3, 4, 8], 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)))}

A214705 Primes that contain only the digits (2, 5, 7).

Original entry on oeis.org

2, 5, 7, 227, 257, 277, 557, 577, 727, 757, 2557, 2777, 5227, 5527, 5557, 7577, 7727, 7757, 22277, 22727, 22777, 25577, 27277, 27527, 52727, 52757, 57527, 57557, 57727, 72227, 72277, 72577, 72727, 75227, 75277, 75527, 75557, 75577, 77527, 77557, 222527, 222557

Offset: 1

Vincenzo Librandi, Jul 28 2012

The digits are prime numbers.

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Subsequence of A019546.

Cf. A385768 - A385800.

[p: p in PrimesUpTo(100000) | Set(Intseq(p)) subset [2,5,7]];

Flatten[Table[Select[FromDigits/@Tuples[{2,5,7},n],PrimeQ],{n,6}]]

from sympy import primerange
def ok(p): return set(str(p)) <= set("257")
def aupto(limit): return [p for p in primerange(2, limit+1) if ok(p)]
print(aupto(222557)) # Michael S. Branicky, Feb 05 2021

A386137 Primes having only {1, 6, 8, 9} as digits.

Original entry on oeis.org

11, 19, 61, 89, 181, 191, 199, 619, 661, 691, 811, 881, 911, 919, 991, 1181, 1619, 1669, 1699, 1811, 1861, 1889, 1999, 6199, 6619, 6661, 6689, 6691, 6869, 6899, 6911, 6961, 6991, 8111, 8161, 8191, 8669, 8681, 8689, 8699, 8819, 8861, 8969, 8999, 9161, 9181, 9199

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A363023, A385782, A385783, A385800.

Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{1, 6, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 6, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("1689"), 41))) # uses function/imports in A385776

A386167 Primes having only {2, 6, 8, 9} as digits.

Original entry on oeis.org

2, 29, 89, 229, 269, 829, 929, 2269, 2689, 2699, 2969, 2999, 6229, 6269, 6299, 6689, 6829, 6869, 6899, 8269, 8629, 8669, 8689, 8699, 8929, 8969, 8999, 9629, 9689, 9829, 9929, 22229, 22669, 22699, 26669, 26699, 28229, 28289, 28669, 29269, 29629, 29669, 29989, 62299

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A385788, A385790, A385800.

Cf. A000040, A030433, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 6, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 6, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 6, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("2689"), 41))) # uses function/imports in A385776

A386186 Primes having only {3, 6, 8, 9} as digits.

Original entry on oeis.org

3, 83, 89, 383, 389, 683, 839, 863, 883, 983, 3389, 3833, 3863, 3889, 3989, 6389, 6689, 6833, 6863, 6869, 6883, 6899, 6983, 8363, 8369, 8389, 8663, 8669, 8689, 8693, 8699, 8839, 8863, 8893, 8933, 8963, 8969, 8999, 9689, 9833, 9839, 9883, 33863, 33889, 33893, 36383

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A385791, A385792, A385800.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [3, 6, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{3, 6, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [3, 6, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("3689"), 41))) # uses function/imports in A385776

A386198 Primes having only {5, 6, 8, 9} as digits.

Original entry on oeis.org

5, 59, 89, 569, 599, 659, 859, 5569, 5659, 5669, 5689, 5869, 6569, 6599, 6659, 6689, 6869, 6899, 6959, 8599, 8669, 8689, 8699, 8969, 8999, 9689, 9859, 55589, 55889, 56569, 56599, 56659, 56989, 56999, 58699, 58889, 59659, 59669, 59699, 59999, 65599, 65699, 65899

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A385797, A385798, A385800.

Cf. A000040, A030433, A106111, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [5, 6, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{5, 6, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [5, 6, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("5689"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A107666 Primes having only {4, 6, 9} as digits.

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A199342 Primes having only {2, 3, 4} as digits.

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A199345 Primes having only {3, 4, 5} as digits.

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

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A199348 Primes having only {3, 4, 8} as digits.

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A214705 Primes that contain only the digits (2, 5, 7).

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A386137 Primes having only {1, 6, 8, 9} as digits.

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A386167 Primes having only {2, 6, 8, 9} as digits.

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