A020466 -id:A020466 - cp's OEIS frontend

A036945 Smallest n-digit prime containing only the digits 4 and 9, or 0 if no such prime exists.

0, 0, 449, 4999, 44449, 444449, 4444949, 44444999, 444499949, 4444444999, 44444449949, 444444494449, 4444449444949, 44444444449499, 444444444499499, 4444444444444999, 44444444444444999, 444444444449449949

Offset: 1

Patrick De Geest, Jan 04 1999

			44449 is the least prime of 5 digits containing just digits 4 and 9 so a(5) = 44449. - _David A. Corneth_, Oct 10 2019

David A. Corneth, Table of n, a(n) for n = 1..538

Cf. A036229, A020466, A036319, A036929-A036951.

Join[{0,0},Table[SelectFirst[10*FromDigits[#]+9&/@Tuples[{4,9},n],PrimeQ],{n,2,20}]] (* Harvey P. Dale, Aug 20 2021 *)

a(n) = my(s=4*(10^(n)-1)/9);forstep(i=1, 2^n-1, 2, fr = fromdigits(5 * binary(i)) + s; if(isprime(fr), return(fr))); 0 \\ David A. Corneth, Oct 10 2019

A368337 Semiprimes that contain only digits 4 and 9.

Original entry on oeis.org

4, 9, 49, 94, 949, 4449, 4499, 9449, 44494, 44949, 44999, 49949, 94499, 94994, 99449, 99494, 99949, 444494, 444949, 494449, 494999, 499949, 944494, 944949, 944999, 949999, 994999, 999494, 4444449, 4444499, 4449949, 4449999, 4494449, 4494499, 4494949, 4494999, 4499449, 4499494, 4944449, 4944499

Offset: 1

Zak Seidov and Robert Israel, Dec 21 2023

The only terms that are squares are 4, 9 and 49.

Numbers of n-digit terms for n = 1...20: {2, 2, 1, 3, 13, 11, 31, 39, 78, 159, 383, 541, 1302, 2047, 4268, 6926, 16248, 27172, 57397, 94581}.

			a(3) = 49 is a term because 49 = 7^2 is a semiprime with digits 4 and 9.

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

Intersection of A001358 and A284973.

Cf. A020466.

R:= 4,9:
for d from 2 to 6 do
  for x from 0 to 2^d-1 do
    L:= convert(2^d+x,base,2)[1..d];
    y:= add((L[i]*5+4)*10^(i-1),i=1..d);
    if numtheory:-bigomega(y)=2 then R:= R,y; fi
od od:
R;

A386349 Primes without {4, 9} as digits.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 61, 67, 71, 73, 83, 101, 103, 107, 113, 127, 131, 137, 151, 157, 163, 167, 173, 181, 211, 223, 227, 233, 251, 257, 263, 271, 277, 281, 283, 307, 311, 313, 317, 331, 337, 353, 367, 373, 383, 503, 521, 523, 557, 563, 571

Offset: 1

Jason Bard, Jul 20 2025

Intersection of A038612 and A038617.

Cf. A000040, A020466, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 3, 5, 6, 7, 8]];

Select[Prime[Range[120]], DigitCount[#, 10, 4] == 0 && DigitCount[#, 10, 9] == 0 &]

primes_with(, 1, [0, 1, 2, 3, 5, 6, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("01235678"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A036945 Smallest n-digit prime containing only the digits 4 and 9, or 0 if no such prime exists.

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A368337 Semiprimes that contain only digits 4 and 9.

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A386349 Primes without {4, 9} as digits.

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