A020466 -id:A020466 - cp's OEIS frontend

A199349 Primes having only {3, 4, 9} as digits.

3, 43, 349, 433, 439, 443, 449, 499, 3343, 3433, 3449, 3499, 3943, 4339, 4349, 4493, 4933, 4943, 4993, 4999, 9343, 9349, 9433, 9439, 9949, 33343, 33349, 33493, 34439, 34499, 34939, 34949, 39343, 39439, 39443, 39499, 43399, 43499, 43933, 43943, 44449, 44939, 49333, 49339, 49393, 49433, 49499, 49939, 49943, 49993

Offset: 1

M. F. Hasler, Nov 05 2011

A020461 and A020466 are subsequences. - Vincenzo Librandi, Jul 30 2015

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

Cf. Primes that contain only the digits (3,4,k): A199340 (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8).

Cf. A020449 - A020472, A199325 - A199329.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [3, 4, 9]]; // Vincenzo Librandi, Jul 30 2015

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {3, 4, 9}]=={} &] (* Vincenzo Librandi, Jul 30 2015 *)
Select[Flatten[Table[FromDigits/@Tuples[{3,4,9},n],{n,5}]],PrimeQ] (* Harvey P. Dale, May 02 2023 *)

a(n, list=0, L=[3,4,9], 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=vecextract(L,v)*u) || next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))}

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

Original entry on oeis.org

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

A260271 Primes having only {1, 4, 9} as digits.

Original entry on oeis.org

11, 19, 41, 149, 191, 199, 419, 449, 491, 499, 911, 919, 941, 991, 1499, 1949, 1999, 4111, 4441, 4919, 4999, 9199, 9419, 9491, 9941, 9949, 11119, 11149, 11411, 11491, 11941, 14149, 14411, 14419, 14449, 19141, 19441, 19919, 19949, 19991, 41141, 41149, 41411

Offset: 1

Vincenzo Librandi, Jul 23 2015

A020452, A020457 and A020466 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. similar sequences listed in A260266.

Cf. A020452, A020457, A020466.

[p: p in PrimesUpTo(5*10^4) | Set(Intseq(p)) subset [1, 4, 9]];

Select[Prime[Range[5 10^3]], Complement[IntegerDigits[#], {1, 4, 9}]=={} &]

A385768 Primes having only {0, 4, 9} as digits.

Original entry on oeis.org

409, 449, 499, 4049, 4099, 4409, 4909, 4999, 9049, 9949, 40009, 40099, 40499, 40949, 44449, 44909, 49009, 49409, 49499, 49999, 90499, 94009, 94049, 94099, 94949, 94999, 99409, 400009, 400409, 400949, 404009, 404099, 404449, 409099, 409499, 409909, 409999

Offset: 1

Jason Bard, Jul 09 2025

			4099 is a term because it is prime, and it only contains {0,4,9}.

Cf. A000040, A020466, A385776.

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

Select[FromDigits/@Tuples[{0,4,9},5],PrimeQ]

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

print(list(islice(primes_with("049"), 41))) # uses function/imports in A385776

A261183 Primes having only {4, 7, 9} as digits.

Original entry on oeis.org

7, 47, 79, 97, 449, 479, 499, 797, 947, 977, 997, 4447, 4799, 4999, 7477, 7499, 7949, 9479, 9497, 9749, 9949, 44449, 44497, 44777, 44797, 47497, 47777, 47779, 47797, 47947, 47977, 49477, 49499, 49747, 49999, 74449, 74747, 74779, 74797, 77447, 77477, 77479

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020465, A020466 and A020471 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..20000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
Index to entries for primes with digits in a given set

Cf. similar sequences listed in A261181.

Cf. A000040, A020465, A020466, A020471.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [4, 7, 9]];

Select[Prime[Range[6 10^4]], Complement[IntegerDigits[#], {4, 7, 9}] == {} &]

A385785 Primes having only {2, 4, 9} as digits.

Original entry on oeis.org

2, 29, 229, 449, 499, 929, 2999, 4229, 4999, 9929, 9949, 22229, 24229, 24499, 29429, 42299, 42499, 42929, 44249, 44449, 49429, 49499, 49999, 94229, 94949, 94999, 99929, 222499, 224299, 224429, 224449, 224929, 229249, 229499, 229949, 242449, 242999, 244429

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020460, A020466.

Cf. A000040, A030433, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 4, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 4, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 4, 9]) \\ uses function in A385776

print(list(islice(primes_with("249"), 41))) # uses function/imports in A385776

A385793 Primes having only {4, 5, 9} as digits.

Original entry on oeis.org

5, 59, 449, 499, 599, 4549, 4999, 5449, 9949, 44449, 44549, 44959, 45599, 45949, 45959, 49459, 49499, 49549, 49559, 49999, 54449, 54499, 54559, 54949, 54959, 55949, 59999, 94559, 94949, 94999, 95549, 95959, 99559, 444449, 445499, 449459, 449549, 449959, 455599

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020466, A020468.

Cf. A000040, A030433, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 5, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 5, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 5, 9]) \\ uses function in A385776

print(list(islice(primes_with("459"), 41))) # uses function/imports in A385776

A385796 Primes having only {4, 8, 9} as digits.

Original entry on oeis.org

89, 449, 499, 4889, 4999, 8849, 8999, 9949, 44449, 48449, 48889, 48989, 49499, 49999, 84449, 84499, 88499, 89449, 89849, 89899, 89989, 94849, 94889, 94949, 94999, 98849, 98899, 98999, 99989, 444449, 448999, 449989, 484489, 484999, 489449, 489989, 494849, 494899

Offset: 1

Jason Bard, Jul 13 2025

Subsequence of A030433.
Supersequence of A020466, A020472.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("489"), 41))) # uses function/imports in A385776

A284973 Numbers with digits 4 and 9 only.

Original entry on oeis.org

4, 9, 44, 49, 94, 99, 444, 449, 494, 499, 944, 949, 994, 999, 4444, 4449, 4494, 4499, 4944, 4949, 4994, 4999, 9444, 9449, 9494, 9499, 9944, 9949, 9994, 9999, 44444, 44449, 44494, 44499, 44944, 44949, 44994, 44999, 49444, 49449, 49494, 49499, 49944, 49949

Offset: 1

Jaroslav Krizek, Apr 07 2017

Prime terms are in A020466.

Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), A284971 (k = 7), A284972 (k = 8), this sequence (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 9}]

a(n,{p=[4,9]})={my(v=binary(n+1));fromdigits(vector(#v-1,i,p[2]*v[i+1]+p[1]*!v[i+1]))} \\ R. J. Cano, Apr 09 2017

A036319 Composite numbers whose prime factors have no digits other than 4's and 9's.

Original entry on oeis.org

201601, 224051, 249001, 2244551, 2494501, 4467101, 4964551, 19957601, 22180051, 22225051, 22449551, 24700001, 24949501, 24990001, 42632101, 42654551, 47379551, 47404501, 49735051, 90518849, 98982601, 100598899, 111801449, 124251499, 199557601, 221780051, 222200551, 247445501

Offset: 1

Patrick De Geest, Dec 15 1998

Closed under multiplication. - David A. Corneth, Sep 21 2020
From M. F. Hasler, Sep 22 2020: (Start)
Also closed under LCM, but not under GCD.
All terms are congruent to 1 or 9 (mod 10), depending on the parity of their number of prime factors counted with multiplicity, A001222. (End)

			The smallest prime made up of 4's and 9's is 449 (see A020466), so the smallest term here is 449^2 = 201601. - _N. J. A. Sloane_, Sep 21 2020

David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for sequences related to prime factors.

Cf. A001222, A020466, A036302-A036325.

cn49Q[n_]:=Module[{fi=FactorInteger[n][[All,1]]},CompositeQ[n]&&Union[ Flatten[ IntegerDigits/@fi]]=={4,9}&&AllTrue[fi,PrimeQ]]; Select[Range[ 1,1006*10^5,2],cn49Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2020 *)

is(N)={!isprime(N)&& !#setminus(Set(concat(apply (digits, factor(N)[,1]))), [4,9])} \\ M. F. Hasler, Sep 22 2020

Sum_{n>=1} 1/a(n) = Product_{p in A020466} (p/(p - 1)) - Sum_{p in A020466} 1/p - 1 = 0.00001523788893... . - Amiram Eldar, May 22 2022

More terms from David A. Corneth, Sep 21 2020

cp's OEIS Frontend

A199349 Primes having only {3, 4, 9} as digits.

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

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A260271 Primes having only {1, 4, 9} as digits.

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Magma

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A385768 Primes having only {0, 4, 9} as digits.

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Magma

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A261183 Primes having only {4, 7, 9} as digits.

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Magma

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A385785 Primes having only {2, 4, 9} as digits.

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Magma

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A385793 Primes having only {4, 5, 9} as digits.

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Magma

Mathematica

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Python

A385796 Primes having only {4, 8, 9} as digits.

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